JAS

382

Volume 106

Number 2

Summer 2020

Journal of the

WASHINGTON

MCZ LIBRARY

ACADEMY OF SCIENCES OCT 22 2020

HARVARD UNIVERSITY

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Presenting the 2020 summer issue of the Journal of the Washington

Academy of Sciences.

There are four papers in this issue plus two interesting Science Bites.

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Calculating Local Group Dark Energy using Better

Mass Data:

Cosmological (and Pedagogical) Results

G. Byrd* and P. Teerikorpi**

*Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL

**Tuorla Observatory, Department of Physics and Astronomy,

Abstract

The Local Group (LG)’s mass is mostly in Andromeda (M31) and the

Milky Way (MW), a central 0.75 Mpe (2.4 MLY) bound binary of mass

M. Dark energy (DE) density “antigravity” causes an outward

acceleration (greater with radius R) of the dwarf population relative to

M’s inward gravitation. The LG’s dwarfs show an increasing outer

velocity (V) component with R in observations. We compare the data to

a local theoretical curve using cosmologically estimated “ACDM”

values. Observations by the WMAP and others give a value of 1.0803 for

the critical density (universe expands forever). The cosmologically

determined DE density is ~0.7 of critical density. The MW-—M31 binary

mass can be estimated from their first moving apart nearly radially and

now approaching. We choose a more recent LG mass~4x10" to calculate

a V vs R line using the cosmologically determined ACDM DE density.

An excellent fit to the data is obtained. Smaller masses give poorer fits.

Assuming the DE = 0 and mass 4x10!’, gives a bad fit to the data. It

appears the DE local density is the same as found cosmologically with no

support for variation with time. DE acceleration in the Local Group

provides an alternative and perhaps more convincing demonstration on a

local scale for students than cosmological estimates.

Introduction

WE FIRST BRIEFLY REVIEW how dark energy’s (DE’s) existence and value

is inferred “cosmologically” from distant galaxies using la supernovae and

analysis of CMB anisotropies. Alternative explanations requiring no dark

energy typically refer to large scales with expected DE effects on small

scales. In light of these results, expected non-zero DE effects on dynamics

in the Local Group (LG) can be an important test of the cosmologically

obtained model.

Summer 2020

Cosmologically Deduced Dark Energy

Dark energy was discovered observationally by studying distances

and redshifts of galaxies at impressively large cosmic look-back times into

the past (Riess et al. 1998, Perlmutter ef al. 1999). The primary methods use

white dwarf supernovas to estimate the large light travel time distances of

galaxies. Shift of recession is a fraction of the speed of light, z = (Aobserved —

Aemitted)/ emitted. The method compares intensity (apparent magnitude) and

known luminosity (absolute magnitudes) to estimate distances.

The well-known linear Hubble Law expresses redshift velocities (V

= cz) versus light travel distances, D, of “nearby” galaxies. Here c is the

speed of light and z is the fractional redshift. Figure | shows a plot of these

two quantities for nearby galaxies from Reiss et a/ (1998). This graph

portrays the concept of the expanding universe. Among the plotted points a

straight line from point one at V= 0, D = 0 to point two is drawn among data

points in a best fit. For this example, the slope gives a Hubble Constant, Ho

= V/D = 65000/940 = 69 (km/s)/Mpc. Here 1 Mpc =3.26 million light years.

70000

ese hea FEE] Na

SERS fos se

60000 ee] a as fog)

50000

40000

30000

RUST SEN Se OA eee Wee

D382 DES Nae

Radial velocity (km/sec)

20000

SNS AMS DAed Gee ws See

10000

00 200 300 400 500 600 700 800 900 1000

0 1

(millions of pe)°*""~

Figure 1. The linear Hubble Law expresses redshift velocities (cz) versus

light travel distances of “nearby” galaxies from Reiss ef al (1998).

The expansion of the universe had its inception in a big bang which

would be slowed by the mutual gravitational attraction of its contents. Using

many nearby galaxies, much effort was made to find the Hubble constant

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slope and any curvature of the plot due to gravitation. Data for much more

distant galaxies was sought to measure the matter content of the universe.

A Riess ef al. 1998, Perlmutter et a/. 1999 data plot is given in Figure

2. The curve represents a uniformly expanding universe with no

gravitational slowing or repulsion. There is a bit of curvature due to

relativity. Mathematically the light travel (proper) distance

d=(cz/H,)(1+z/2)/(1+z) for the Milne model. See Byrd et al. (2012)

and Irwin (2008). If there is only gravitating matter deceleration, distant

galaxies should be above the curve. As can be seen in Figure 2, the majority

of observed distant points are below the curve. The observations in the graph

indicate properties that are progressively more distant in the past. From the

distributions of data points the acceleration due to “dark energy” DE began

to dominate ~6-7 billion years ago.

600000 5

500000 +

400000 +

300000 +

Redshift cz in km/s

200000 +

100000 -

1} t :

0) 5000 10000 15000 20000

Distance in 10° light years

Figure 2. Non-linear Redshifts at Large Distances found by Type I

supernovae from Riess ef al. (1998) and Perlmutter et al. (1999).

Summer 2020

To give notation and values for the variables, we use the microwave

background 3K “ACDM” values from WMAP (see references Technical

Papers and Cosmological Parameters). The critical density is

p, 29.510 gem =3H; /(8aG):

This density is 1.0803 + 0.085 of the critical flatness density (in which the

universe expands forever) which is designated as (2 = |. Current energy

densities are DE pv = 7 x 10°° g/cm? and matter pm = 3 x 10°° g/cm?

corresponding to Qy = 0.7 and Qm= 0.3. The age of the universe =13.75

billion years. The Hubble constant Ho = 71 (km/s)/Mpce.

As shown in Figure 3, a better fit to the data points requires a DE

acceleration to have the points below the line. Gravitating matter tends to

reduce the effect of DE. The model passing through the middle of the SN Ia

Qy for z < 0.5 with Qy = 0.7 and Qm = 0.3 for the sum = 1 for the critical

density and using

points has both DE and gravitating matter. From Irwin (2007), q =

d =(EqF.16)/(1+z)=(cz/H,)|1+z(1-q)/2 |/(1+z) :

0 5000 10000 15000

Distance in 10° light years

500000 +

”

® 300000 4

200000 4 oa

100000 + ee

pa 7

0 a) T 1 i T T a “7

0 1000 2000 3000 4000 5000 6000

Distance in Mpc

Figure 3. A better fit to the recession versus distance data points with a DE

acceleration to have the points below the line. This is interpreted as

cosmological evidence for dark energy.

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Calculating Local Group Dark Energy using Better Mass Data:

By examining Figure 4 we can see that most of LG’s gravitating

mass (M) is in a 0.75 Mpc central binary. Members M31 and MW orbit the

center of mass (CM). Many dwarf galaxies are left beyond the binary from

formation, others are bound to it. There are also a few low mass galaxies.

LG Properties

Sax

Pst ss

- na

- eB & LY

2Mpc;6.5Mly ene

Figure 4. Plot of Local Group members. By permission of Rami Rekola.

Summer 2020

Local Group Dwarf Equation of Motion and Observations

As diagrammed in Figure 5, in and near the binary center of mass,

dwarf galaxy motions are inward and outward in and near the binary CM

(red/blue arrows). At distance R outside the binary, motions are outward

(red). Relative to the CM, a dwarf’s equation of motion is the central binary

mass, M, gravitational attraction plus the DE density, py, repulsion:

d’R_ GM = 8aG

oye Se ee

dt? Re 3 Ps

The net acceleration ~ 0 at R equals

given by the local “Newtonian” limit of general relativity with DE. (Byrd er

al. 2012).

Figure 5. Dwarf motions relative to the binary center of mass (CM) are

shown. Motions are inward and outward in and near the binary CM

(arrows). At R outside the binary, motions are outward (red) relative to

CM.

Figure 6 shows dwarfs’ observed recession velocities relative to

center of mass of binary versus radius, Chernin eft al. (2009) and

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Karachentsev er al. (2009). The line is an empirical fit to an outer dwarf

outflow region. The gravitationally bound central region shows inner and

outer (positive and negative) motions.

300

HST data: Karachentsev et al. 2009

250 ®

VvsR relative to center of mass

200

¢SagdSph

150 aa

? >

“~ Leol

100

% N6822 pg

BY 4 = Antlia

t gO +

of ——

pDO219, a Outer

~ Tucana... ; poets ;

¥ : mane dwarf outflow

Leow, region. Line is

empirical fit.

Phoenkx

Gravitationally

bound

Se ies central

“t— region

0 0.25 05 0.75 1 1.25 ig 1.75 2 2.25 25 2.75 3

R, Mpc

-100

-150

Figure 6. Dwarfs’ observed wavelength change velocities relative to center

of mass of binary (Chernin ef al. 2009 and Karachentsev ef al. 2009).

Determining DE using Observed Outward Vs at Rs.

Use Outflow V vs R in Figure 6 to estimate DE py. Small members

fly out under LG gravity and DE acceleration. Integrate each dwart’s equation

of motion from small to present-day R & V. Mathematically we get

1/2

V R y)

—— =|| — | +——_-2a@

ED Ws, R RR

where the small initial energy;

’ Vv

82Gp, )

aGM , 2

1/3

= ~=1Mpe and H,=[

8717p,

The subscript v indicates dark energy.

Summer 2020

The time to reach from near the center to the present must be the

approximate age of universe or

1/2

He ny | Ril eilen op Re

ea dR =13.7Gy1 = =] are 2a we

In the above equation choose different dark energy densities, py , to

fit V vs R data from Hubble Space Telescope and the Gaia mission to obtain

M. This permits an improvement in LG mass. The transverse motion of M31

has now been measured (van der Marel et a/. 2019) which permits a better

mass measurement (McLeod et al, 2017). As seen in Figure 7, M31 and MW

receded from one another in the past. The future approach path to merger is

. . . _ 9}

shown. The revised mass estimate is = 3.6 + 0.3 x 10'2 Mo.

O now

> in 25 billion years

X in 45 billion years

Triangulum (M33)

Milky Way

Andromeda (M31)

NS \

1 million light years

Figure 7. Future path to merger of the Milky Way Galaxy and M31.

https://www.esa.int/ESA Multimedia/Images/2019/02/Future motions of

the Milky Way Andromeda and Triangulum galaxies#.XInMdFILDsA

ink

Using better M in V vs R plot to Estimate Local Group DE

As shown in Figure 8, various masses are used to check which one

results in the observed outward Vs at Rs. There 1s a good fit to the observed

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V versus R where R > 1.25 Mpc and the “Cosmological” DE py= 7 x 107°

g/cm? for the best LG M=4 x 10!2 Mo.

300

250

200

150

100

v (km/s)

Karachentsev 2009 —+—

0 0.5 1 1.5 2 2.5 a ie

R (Mpc)

Figure 8. Dwarfs’ observed velocities due to wavelength change relative to

center of mass of binary (Chernin ef a/l.2009 and Karachentsev ef a/. 2009).

Saarinen and Teerikorpi, (2014) calculated V versus R value curves for

different LG masses and “Cosmological” DE py= 7 x 10° g/cm? .

Recall there is a good R, V fit > 1 to 1.5 Mpc with “Cosmological”

DE py=7 x 10°° g/cm? for the better LG M= 4 x 10'? Mo. If pv = 0 g/cm?

the best mass 4 x 10!? Mo line is a poor fit. The mass 2 x 10!” is a good fit

but has too low a mass, two times the estimated uncertainty of 1 x 10'? Mo

away from the better 4 x 10'* Mo. Local DE density doesn’t appear to be

zero. See Figure 9.

Summer 2020

no local DE

Py= 0 g/cm?

v (km/s)

-100

-150

Karachentsev 2009 ———

0 0.5 1 1.5 2 2.5 3 3.€

R (Mpc)

Figure 9—Velocities and for dwarf LG masses and py = 0 g/cm*. Up-to-

date LG mass 4 x 10!” Mo line is a poor fit.

Conclusions

The better mass ~ 4 x 10!? Mo for the LG and dwarfs’ V vs R do not

support zero local dark energy (Figure 9). The “local” dark energy estimate

is consistent with cosmologically distant estimates (Figure 8). A recent

determination using a galaxy survey combined with other methods agrees

with the accepted cosmological value, (Nadathur, ef a/. 2020). Also see Byrd

ef ai (2015, Sec: 8) tor va list of valties determined) at gz as larce as 3.

Agreement of cosmological and local values implies no change with time

indicating there is no future “big rip”.

DE acceleration in LG is possibly a more understandable argument

for DE than cosmological evidence. Student demonstrations of an expanding

dark energy universe follow.

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Appendix: Student Demonstrations

“Big Band” Universe Expansion Demonstration. Figure 10a, b shows a

large rubber band with a uniform distribution of “Bull Dog” clip “galaxies”

and their gravitation. Stretching between hands is “dark energy repulsion”.

Elastic resistance is of the band is “uniform matter gravitation”. As the band

is stretched, we see uniform relative motion of the galaxies away from one

another. A video link is also given.

Figure 10a, b

Bull Dog clip “galaxies” and their gravitation. Video link.

https://drive.google.com/file/d/1782jMilbgeccwyVcymFj]BOPYaEfSe6Y 3/

view?usp=drivesdk

A uniform large rubber band with a uniform distribution of

Figure | la, b shows a large rubber band with an initially uniform distribution

of Bull Dog clip “galaxies.” However, two massive galaxies have a greater

gravitational force represented by an additional strand between them. These

represent the Local Group binary members, the Milky Way and M31. Again,

stretching between bands is “dark energy repulsion”. However, elastic

“oravitational” resistance is of the band is non-uniform because it is greater

between the binary members. As the band is stretched, we see the binary

members hardly moving away from one another and the outer dwarf

members receding from the binary at progressively larger distances as “dark

energy” stretches space (the band). A video link is also given.

Summer 2020

2 fool te Vs tes a

4 Double Strand M 7m

Figure | 1a, b -- A large rubber band with an initially uniform distribution

of bull dog clip “galaxies.” However, two galaxies have a greater

gravitational force represented by an additional strand between them.

https://drive.google.com/file/d/1706_eld6Dd9e9 Y Os9Op2pZ9-

FoMjsrxJ/view?usp=drivesdk

References

Byrd, G., Chernin, A. D., Teerikorpi, P. and Valtonen, M. 2012 Paths to

Dark Energy, De Gruyter, Berlin/Boston, ISBN 978-3-11-025854-

TeSece. devi, 300

Byrd, G., Chernin, A., Teerikorpi, P. and Valtonen, M. 2015, Review

Article: “Observations of General Relativity at strong and weak

limits” in General Relativity: The most beautiful of theories (De

Gruyter Studies in Mathematical Physics) 2015. ISBN-10:

3110340429; ISBN-13: 978-3 110340426

Chernin, A.D., Bisnovatyi-Kogan, G. S., Teerikorpi, P., Valtonen, M. J.,

Byrd, G. G. and Merafina, M. 2013 “Dark energy and the structure

of the Coma cluster of galaxies,” Astronomy and Astrophysics, 553

(2013), A101:1—-A101:4.

Chernin, A. D., Teerikorpi, P., Valtonen, M. J., Dolgachey, V. P.,

. Domozhilova, L. M. and Byrd, G. G. 2009 “ Local dark matter and

dark energy as estimated on a scale of ~ 1 Mpc in a self-consistent

way Astron. & Astrophys., 507, 1271. (and references

https://www.esa.int/ESA_ Multimedia/Images/2019/02/Future motions of

the Milky Way Andromeda and Triangulum_galaxies#.XInMd

FILDsA.link

Irwin ,J. 2007 Astrophysics: Decoding the Cosmos John Wiley and Son,

West Sussex, England ISBN 978-470-01306-9.

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Karachentsev, I.D., Kashibadze, O.G., Makarov, D.I., Tully, R.B. 2009,

MNRAS, 393, 1265 https://arxiv.org/pdt/08 11.4610.pdf

https://ned.ipac.caltech.edu/cgi-

bin/objsearch?search_type=Search&refcode=2009MNRAS.393.12

65K

McLeod, M. and Libeskind, N. and Lahav, O. & Hoffman, Y. 2017, Dec.

“Estimating the Mass of the Local Group Using Machine Learning”

Journal of Cosmology and Astroparticle Physics 34.

https://arxiv.org/pdf/1606.02694.pdf

Nadathur, S., Percival, W. J., Beutler, F., Winther,, H, A. 2020, Physical

Review Letters. Phys. Rev. Lett. 124, 221301 DOI:

10.1103/PhysRevLett.124.221301 Also see

https://scitechdaily.com/most-precise-tests-of-dark-energy-and-

cosmic-expansion-yet-confirm-the-model-of-a-spatially-flat-

universe/

Perlmutter et al. 1999, The Astrophysical Journal, 517, 565-586

Riess, A. G. et al 1998 The Astronomical Journal, 116, Issue 3, 1009

https://arxiv.org/abs/astro-ph/9805201

Saarinen, J. and Teerikorpi, P. 2014, Astronomy and Astrophysics, 568,

A33

van der Marel, R.P.,Fardal, M. A., Sohn, T. S., Patel, E., Besla, G., del

Pino, A., Sahlmann, J. and Watkins, L. L. 2019 The Astrophysical

Journal, 872,24 https:/iopscience.iop.org/article/10.3847/1538-

4357/ab001b

WMAP Technical papers can all be found at:

http://lambda.gsfc.nasa.gov/product/map/current/map_bibliography

WMAP Cosmological Parameters based on the latest observations:

http://lambda.gsfce.nasa.gov/product/map/current/parameters.cfm

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BIO

Gene Byrd (B.S Texas A&M Univ. 1968; PhD 1974 the Univ. of Texas) is

a Professor of Astronomy (emeritus) at the Univ. of Alabama. He studies the

dynamics of galaxies, discovering the pattern in NGC4622, which, counter-

intuitively, has inner and outer spiral arms winding in opposite directions

See https://www.researchgate.net/profile/Gene_Byrd2 .

Pekka Teerikorpi received his doctorate at the University of Turku (1981).

After teaching and research positions there he is now a retired adjunct

professor. He studies extragalactic astronomy, in particular, the cosmic

distance scale, the expansion of the universe (the Hubble constant) and dark

energy.

Washington Academy of Sciences

Land Footprint of the United States of America

AARON S. HOGUE

Salisbury University

ABSTRACT

Globally more than a quarter of all evaluated species are threatened with

extinction, and the numbers continue to grow. Studies suggest habitat loss,

driven predominantly by human land use, is the primary cause. The goals of

this study are to examine the contribution of the United States of America (US)

to habitat loss by quantifying its domestic land footprint (area of land altered

from its natural state for human use), and to identify changes in human

behavior that can reduce this footprint. Land use data for the US were

compiled for the focal year 2012 and partitioned into 14 consumption

categories. When all combined, the domestic land footprint in 2012 was

5,510,576 km’, an area equivalent to 72% of the contiguous US. Although this

is likely an underestimate (for reasons outlined below), if everyone on earth

averaged the per capita footprint of Americans, the global human land

footprint would exceed all ice-free land on Earth. Thus, the US population

damages ecosystems on scales vastly greater than what is proportional or

sustainable. Of the total domestic land footprint 71% is for meat/animal

production. Given it takes 4-140 times more land to produce the same amount

of protein and calories from meat as it does from plants, replacing meat with

plant protein could eliminate the majority of the US land footprint, exceeding

the land savings of all other conceivable actions combined.

INTRODUCTION

OF THE SPECIES THAT HAVE BEEN EVALUATED over 30,000 are threatened

globally with extinction, due primarily to the actions of humans (IUCN

2020). That’s more than one quarter of all species assessed (IUCN 2020).

The severity of this crisis is reinforced by a consideration of recent

extinctions. A number of studies comparing recent rates of extinction

(largely driven by human activity) to background rates documented in the

fossil record suggest current rates are hundreds of time higher than normal,

placing us in the midst of one of the six greatest mass extinction events in

earth history (Leakey & Lewin 1992; Dirzo & Raven 2003; Barnosky et al.

ZOU);

Recognition of the urgent need for action led to the global ratification

of the Convention on Biological Diversity (CBD) in 1992. The goal of this

and subsequent international efforts was to significantly reduce rates of

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biodiversity loss, with specific targets for both 2010 and 2020 (Hoffmann ef

al. 2010; Tittensor ef al. 2014). Despite these efforts, an examination of 31

indicators established to evaluate biodiversity declines found no significant

reduction in rates of decline, and an overall failure to achieve the 2010

Target (Butchart et al. 2010). A detailed analysis of birds, mammals, and

amphibians in the years leading up to 2010 (1980-2008) found all three

groups showed net increases in the probability of extinction with, on

average, 52 species moving “I Red List category closer to extinction” per

year (Hoffmann ef al. 2010). Similarly, a mid-term analysis of progress

toward the 2020 Target found biodiversity declines continue, and projected

that the 2020 Target also will not be achieved (Tittensor et a/. 2014).

Subsequent work has continued to find substantial reductions in population

sizes, species ranges, and biodiversity across the globe (Ceballos et al 2017;

Grooten & Almond 2018), leading Ceballos et a/. (2017) to describe the

current state of affairs as an unprecedented “biological annihilation.” Not

only does this mean the future of large numbers of species remains very

much in doubt, but as more species disappear from ecosystems, this will, in

turn, have profound negative impacts on the health of these ecosystems and

the human populations that depend on them (Cardinale et a/. 2012; Hooper

et al 2012).

Given the gravity of the situation, it 1s important to act swiftly and

reduce the major factors responsible for these biodiversity declines. And

what are these major factors? A number of studies have attempted to answer

this question using data from the International Union for the Conservation

of Nature (IUCN). The IUCN is the World’s pre-eminent global

conservation body, and maintains the Red List, the single most authoritative

and comprehensive list of all species scientifically identified as threatened

with extinction (IUCN 2020). Contrary to the near single-minded focus by

the US media and political elite on climate change, analyses of this database

and other sources have consistently found habitat loss exceeds other threats

as the most significant (Venter et al. 2006; Vie et al. 2009; Pereira ef al.

2012; Tittensor et al 2014; Grooten & Almond 2018). More specifically, it

is human land use that poses the greatest threat to species (Tittensor ef al.

2014; Maxwell et al. 2016).

It is beyond the scope of this work to review the status of the Earth’s

ecosystems, but to give some sense of the extent of human impact, 53% of

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Earth’s ice-free land has been modified from native ecosystems to human-

dominated landscapes (Hooke er a/. 20012) and 75% of land area globally

has been measurably impacted by human activities (Venter ef al. 2016).

Most of the remaining 25% of minimally disturbed land consists of low

biodiversity deserts, tundra, and boreal forests. As the global population is

projected to increase from 7.7 billion to 11 billion by the end of the century

(United Nations 2019), with each additional person requiring more land for

food, energy, space, and other resources (Gibbs ef a/. 2010; d’ Amour ef al.

17), this means habitat loss and ecosystem degradation from additional land

conversion will continue to grow unless we identify strategies to reduce the

problem.

An important part of moving in the right direction on land use

involves several things: quantifying current land use, determining which

human activities require the most land, and identifying practical changes in

human activities that can significantly reduce the need for land. Nowhere is

this more important than in the US. The US has a vastly higher

environmental impact than nearly every other country on the planet, both on

a per capita and national basis (Bradshaw ef al. 2010; Simas ef al. 2017), so

changes in this country can yield dramatic reductions in land use and habitat

loss. The purpose of this study 1s to use a variety of data sources to obtain a

minimum, conservative estimate of the amount of land within the US

significantly impacted by human activities and partition it into discrete

categories reflecting specific aspects of American culture (America and

American as used herein are meant to refer to the United States and its

population). These data will then be used to identify concrete, yet feasible

actions that can dramatically lessen the environmental impact of the US. The

focus was limited to domestic land footprint data because adequate, accurate

data for most imports and US activities abroad were not available. Given the

hundreds of foreign US military bases (Vine 2015), and the fact that there

was a $537 billion trade deficit in the focal year of this study (US Census

Bureau 2019), the overall footprint computed is likely an underestimate of

our actual footprint.

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METHODS

Primary data sources were limited to the most accurate, most

comprehensive available for the year 2012 that provide as close to a full

picture as possible of the minimum footprint of US Citizens without double

counting. The year 2012 was selected because it was the only recent year for

which several comprehensive datasets were simultaneously available: a GIS

database partitioning land into discrete use categories (residential,

transportation, commercial, efc. - Theobald 2014) and several infrequently

released government databases containing land use information. The latter

included the 2012 Grazing Statistical Summary (USDA 2013), 2012

Agricultural (Ag) Census (USDA 2014), 2012 Natural Resources Inventory

(USDA 2015), and the 2012 Forest Resources of the United States (Oswalt

et al. 2014). These datasets served as the starting point for all footprint

calculations, with refinements derived from other governmental and

nongovernmental sources noted below. Only lands modified from their

natural state for human use were included in the footprint calculations (e.g.,

lands for buildings, roads, lawns, timber harvests, grazing, crops). The

footprint calculations do not include lands indirectly impacted by human

activity, such as habitat degradation due to fragmentation or wildlands

burned by human-caused fires. It is therefore a conservative estimate of the

United States’ most direct and most significant impact on domestic

terrestrial ecosystems. Based on these and other sources, land footprint data

largely fell into two major categories: Non-Biomass Developed Land and

Biomass Production Land. Each of these two main categories and associated

sub-categories are described separately below.

Non-Biomass Developed Land

Developed land consists of built land (e.g., buildings, concrete,

asphalt), but may also include some surrounding open areas created and

maintained by humans (e.g., mowed turfgrass). The most thorough source

for total area of developed land in 2012 is the National Resources Inventory,

or NRI (USDA 2015). The NRI is a scientifically robust inventory of non-

Federal US lands based on a rotational sampling of 800,000 points spread

across the US and its territories, using both satellite imagery and on-the-

ground verification by Natural Resource Conservation Service (NRCS)

staff. The only other data source that approaches the thoroughness of the

NRI is the 2011 National Land Cover Database, or NLCD (Homer et ai.

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2015). The NLCD differs from the NRI in that it relies exclusively on

identifying land cover from high resolution (30x30 meter) satellite imagery.

Both datasets yield very similar numbers (differing by less than 1% in

overlapping areas), but given the NLCD is from 2011, not 2012, and is

exclusively satellite-based without ground verification (the lack of which

tends to underestimate developed land — Theobald 2014), the NRI is used as

the primary source, with the NLCD used to fill gaps in the NRI database.

One such gap is that the NRI does not quantify developed land in Alaska or

federal properties. To partially fill this gap estimates of developed land for

Alaska and federal military bases in the conterminous US were obtained

from the NLCD (using the partitioning process described below) and added

to the NRI data to obtain an estimate of total US developed land. As the

NLCD data are from the year prior, and do not include all federal lands, this

total must be viewed as an underestimate of total developed land in 2012.

One limitation of both the NRI and NLCD is that they do not

partition developed land according to more specific land use categories.

While this limitation cannot be completely overcome, the use of an

additional dataset in combination with the NLCD allows one to subdivide a

significant fraction of developed land, at least in the conterminous US.

Theobald (2014) used US Census data and other sources for the

conterminous US to categorize the same 30x30m blocks examined in the

NLCD as belonging to one of 80 land use categories. The resulting National

Land Use Database (NLUD) was then used to estimate America’s land

footprint within the conterminous US (Theobald 2014). Unfortunately, this

approach overestimates our direct land footprint because census-designated

property boundaries for many land uses (e.g., residential, commercial) may

contain a mixture of both human-modified and natural land covers, such as

built land and forest, respectively. However, by combining these two

datasets, it is possible to partition satellite-designated developed land into

more discrete land uses.

This was accomplished by using ArcGIS 10.3 to cross-tabulate each

30x30m plot designated as developed in the NLCD with its land use

designation in the NLUD. Area measures for similar land use (LU) codes

were then combined into one of the following 10 categories (LU codes from

Theobald 2014): Water use/access (e.g., boat ramps, hardened shorelines,

dams; LU codes 111-172,419, 519,522-523), Outdoor Recreation &

Summer 2020

Resources (e.g., parks, golf courses; LU codes 341,410-417,421-

422,518,532), Conservation (e.g., nature reserves, archaeological sites; LU

codes 511-516,521,531), Residential (e.g., housing; LU codes 211-215),

Commercial (e.g., offices, stores; LU codes 221-223), Industrial (e¢.g.,

factories, mines; LU codes 231,330), Institutional (e.g., schools, hospitals,

government buildings; LU codes 241-249), Major Transportation (e.g.,

airports, major highways and railways; LU codes 251-255), Crop

Infrastructure (e.g., equipment storage, access roads; LU codes 310-

311,313-314), and Livestock Infrastructure (e.g., barns, confined animal

feeding facilities; LU codes 233,312,315,321). All developed plots not

falling into one of the above 10 categories, as well as all developed areas in

Hawaii and Alaska (which were not included in the NLUD), were designated

as “Unassigned.” Crop Infrastructure, Livestock Infrastructure, and

Unassigned lands were then subtracted from total developed land to yield

known Non-Biomass Developed Land. Note: Major Transportation does not

include most small roads or railways. The width of these linear features is

often well under 30m, so they tend to be subsumed under the adjacent land

use. Thus, it should be assumed that the other developed land categories

include their own fraction of transportation land (e.g., residential area

includes driveways and often residential roads).

Biomass Production Land

Biomass Production Land consists of land needed to generate

products that are grown (e.g., crops, animals, timber). It includes non-

developed land used to grow or feed these organisms, as well support lands,

many of which fall under the developed land categories “Crop

Infrastructure” and “Livestock Infrastructure” noted above. Source data for

calculating Biomass Production Land are largely grouped under three land

use categories: timberland, cropland, and grazing land. However, these

categories do not adequately correspond to final end uses by people that

would inform changes in behavior that reduce our environmental impact.

For example cropland is used to make very different things, such as fiber,

fuel, and food. Therefore, data from these initial three categories were

processed to yield six new product categories grouped into two main

subcategories. The first main subcategory is Fuel and Fiber Land, which is

divided into four product categories: Wood Production Land (from timber

land data), Cropland for Fiber, Cropland for Fuel, and Cropland for

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Horticulture (from the cropland data). The second main subcategory is Food

Production Land, which is divided into Cropland for Food (direct human

consumption, from cropland data), and Meat Production Land (which

includes Cropland for Feed and grazing lands). Each is described below,

organized principally by land use source data due to the interconnectedness

of their calculations. However, results will be presented by the main

subcategories and six final product categories noted above.

Timberland (Wood Production Land)

The focus of this study is on lands significantly impacted by human

activity in 2012. Most forests take many decades to return to mature

conditions, let alone natural old growth conditions after harvest (Aide ef al.

2001; Dunn 2004; Meli et a/. 2017). Consequently, forests harvested many

years prior to 2012 may still be viewed as significantly impacted, even if

natural regrowth is occurring. There are data on deforestation rates in the US

in the 12 years leading up to and including 2012, averaging 21,995 km? per

year (Hansen ef al. 2013). If one adopts a conservative assumption that only

forests under 20 years of age continue to show significant human impact

(which is without question an underestimate), one could extrapolate this

figure over the prior two decades to obtain total impacted forest land

(439,907 km?). However, this does not account for that fact that some of

these were converted to other land uses over that time, and are therefore

already counted in footprint data for those other categories. Fortunately, the

USDA maintains data on total area of forest in 2012 that was either cut that

year or under 20 years of age in 2012. These data were used for wood

production land. It is important to note, this doesn’t include major portions

of the 263,837 km of artificially planted forests in the US (Oswalt et al.

2014) that were 20+ years old, particularly monoculture and non-native tree

plantations, all of which qualify as land significantly modified for human

use. Adequate data were not available to include these additional lands in

the analyses. Thus, this is an underestimate of forest land significantly

impacted by humans.

Cropland

In order to determine the amount of land devoted to producing feed

(consumed by livestock), fiber (e.g., cotton, tobacco), biofuels (ethanol and

biodiesel), and food (crops fed to humans), it was first necessary to calculate

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two numbers: total harvested cropland and total non-harvested cropland.

These numbers were obtained from the 2012 Agricultural Census (USDA

2014). Total harvested cropland is the amount of land planted and harvested.

Non-harvested cropland consists of other cropland that was not harvested

(primarily because it failed or was left idle) and crop infrastructure land.

While this latter set of lands did not produce crops, it was nontheless part of

the US cropland footprint.

Harvested lands for feed, fiber, and fuel were calculated as described

below, then subtracted from total harvested cropland to obtain a preliminary

estimate of the amount of land used to produce plant-based food directly

consumed by humans. To determine the amount of non-harvested cropland

and infrastructure land associated with each of these four categories of

harvested crops, the area of harvested land in each category was divided by

total harvested area to obtain the fraction of harvested land in each category.

The fraction for each category was then multiplied by total nonharvested

cropland and added to the harvested area for that category to obtain an

estimate of the total area needed to produce feed, fiber, biofuels, and food.

This approach was adopted to proportionally distribute non-harvested

cropland and infrastructure land among the major categories, as complete

data on the amount of infrastrure, fallow, and failed cropland belonging in

each category were not available. Data for a fifth category of cropland,

horticulture, was also obtained from the Ag Census (USDA 2014). As data

for this category includes harvested and non-harvested land, the total area

was subtracted from the remaining food land.

The area of cropland harvested for fiber was obtained directly from

the Agricultural (Ag) Census (USDA 2014).

Land harvested for biofuels was obtained from USDA data on

diversion of crops for ethanol and biodiesel production. Harvested area for

ethanol production was determined by dividing bushels of corn diverted to

fuel ethanol in 2012 (USDA 2018a) by corn yield estimates for that year

(USDA 2018b). For soy, amounts diverted for fuel are reported in pounds of

oil (USDA 2018a). Since oil makes up approximately 11 Ib of every bushel

(USDA 1988), pounds were divided by 11 to obtain total bushels. Since

soybeans processed for biodiesel also yield economically valuable soybean

meal (soy crush) used as feed, it was necessary to allocate a fraction of these

bushels to each of these coproducts. This study follows Eshel er al. (2014)

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in using an approximate economic and caloric fraction of 40% oil, 60%

meal/crush. The number of bushels was multiplied by 0.4, then divided by

average 2012 yields (USDA 2018c) to obtain total area.

Feed cropland was calculated from USDA data on bushels diverted

for feed along with corresponding yield data. Areas of corn, sorghum,

barley, and oats harvested for feed were calculated from the Feed Grain

Yearbook for 2012 (USDA 2018b). The area of soy and soy crush used for

feed was obtained from the Soy Yearbook for 2012 (USDA 2018c, soy crush

bushels multiplied by 0.6, based on Eshel ef al. 2014). Harvested area for

wheat and rye feed were obtained from the Wheat Data Yearbook Tables

(USDA 2018d). Lastly, area harvested for feed roughage (hay, haylage,

grass silage, greenchop, corn silage, and sorghum silage) were obtained from

the Ag Census (USDA 2014).

Grazing Land (Meat/Animal Production Land)

Meat production land consists of grazing land, livestock

infrastructure land, and cropland for feed. Calculations for the latter two

were described above. Grazing land exists on public and private lands as

pasture (lands managed specifically for grazing) and rangelands (semi-

natural areas not explicitly managed for grazing, but nonetheless modified

by grazing from domestic livestock). Federal grazing land area was

calculated from Bureau of Land Management rangeland area (USDI 2013)

and U.S. Forest Service grazing allotments (USDA 2013). Private

pastureland and rangeland area was obtained from the National Resource

Inventory (USDA 2015).

RESULTS

Non-Biomass Developed Land

The total area of non-federal developed land in the conterminous US

and Hawaii in 2012 was 459,375 km’. Total developed land in Alaska came

to 1,496 km’. Developed land on federal military bases within the

conterminous US covered 3,996 km?. Combined this yields a total minimum

area of developed land within the US of 464,867 km? (Table 1).

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Table 1. Developed land by category.

Land Category Area (km?)

Industrial/Manufacturing 6,528

Commercial 14,510

Institutional/Government 9,886

Major Transportation 36,359

Residential DS 2 97)

Outdoor Recreation & Resources 18,854

Water Use & Access 10,833

Conservation Land 7216

SUBTOTAL: Non-Biomass Developed Land 309,543

Crop Infrastructure 535532

Livestock Infrastructure S2e2 60)

SUBTOTAL: Biomass Production Developed 155,019

Land

SUBTOTAL: Unassigned Development LO 505

TOTAL DEVELOPED LAND 464,867

Results of partitioning developed land into more specific land use

categories are presented in Table 1. After subtracting unassigned lands

(19,505 km?) and developed lands involving biomass production (135,819

km’), total known non-biomass developed lands came to 309,543 km?

(Table 1). Since most assigned developed land fell under the non-biomass

category, for simplicity’s sake, non-biomass and unassigned developed land

are grouped together in subsequent discussions.

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Biomass Production Land

Area of forest land significantly impacted by harvesting (Wood Production

Land) was 375,649.8 km? (Oswalt et al. 2014) (Table 2).

Table 2. US domestic land footprint by major category.

Land Category

Wood Production Land

Cropland for Fuel

Cropland for Fiber

Cropland for Horticulture

SUBTOTAL: Fuel & Fiber Land

Meat/Animal Production Land

Cropland for Feed

Livestock Infrastructure

Private Pastureland

Private Rangeland

BLM Rangeland

FS Grazing Allotments

Cropland for Food

SUBTOTAL: Food Production Land

SUBTOTAL: Non-Biomass Developed

Land (& Unassigned)

TOTAL LAND FOOTPRINT

Nee

Area

(km?)

315,050

225,002

48,756

2,880

653,088

39225198

695,064

82,287

490,229

1,642,122

628,044

384,452

606,241

4,528,439

329,048

3,910,570

% Contiguous

US Land Area

4.9

Dee}

0.6

0.0

8.5

lett

6.4

21.4

8.2

(eS)

59a

4.3

TLD

Summer 2020

Harvested cropland in 2012 was 1,274,618 km? (USDA 2014). Non-

harvested cropland and infrastructure was 304,126 km? (250,594 km* other

cropland — USDA 2014; 53,532 km? crop infrastructure — Table 1).

Harvested fiber land came to 39,363.9 km. This represents 3.1% of

total harvested area. Multiplying this number expressed as a fraction by total

non-harvested cropland puts its portion of this land at 9,392.3 km”, bringing

total fiber cropland & infrastructure to 48,756.2 km? (Table 2).

The total area of harvested biofuel land came to 182,304.1 km7, or

14.3% of all harvested land. Using this to calculate its fraction of non-

harvested land brings its share of the latter to 43,498.0 km’. Thus, total

biofuel production area came to 225,802.1 km? (Table 2).

Horticultural lands consisted of 1,252 km? of Christmas tree

plantations, 1,300.3 km? for sod, and 328 km? floriculture/seed lands (USDA

2014), totaling 2,880.2 km? (Table 2).

Grazing lands were comprised of 490,228.5 km? of private

pastureland (USDA 2015), 1,642,122.3 km? of private rangeland (USDA

2015), 628,044.0 km? BLM rangeland (USDI 2013), and 384,451.7 km?

forest service grazing land (USDA 2013) (Table 2). Harvested feed cropland

consists of 561,168.2 km’, or 44.0% of harvested cropland. Adding its

fraction of non-harvested crop and infrastructure land to this, total area for

feed was 695,063.7 km? (Table 2). Combining these numbers with livestock

infrastructure land, the total area of meat/animal production came to

3,922,198 km? (Table 2).

Subtracting harvested fiber, feed, and fuel land from total harvested

cropland yielded a difference of 491,781.4, or 38.6% of harvested cropland.

Combined with the remaining non-harvested area, a total of 609,121.2 km?

is attributable to food and horticulture. Subtracting the horticulture total

leaves 606,241.0 km? for food (Table 2).

DISCUSSION

These results reveal that the minimum, conservative estimate of the

United States’ domestic land footprint is 5,510,576 km? (Table 2). To put

this in perspective, it is equivalent to nearly 72% of contiguous US land area

(the lower 48 states, excluding Alaska and Hawaii) (Table 2). Note that this

does not include large amounts of land impacted by American activities at

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home and abroad, including land submerged by hydroelectric dams, land

burned from human-caused fires, large tracts of unnatural planted forests

(akin to cropland), all land used outside the US to produce and transport

imported products (including imported meat), roughly 800 foreign military

bases (some the size of small cities — Vine 2015), the United States’ fraction

of land used for tourism abroad, land degraded by habitat fragmentation, and

so on. The only set of data that is likely overestimated here is land identified

as “cropland for food.” Any land used for crop production that was not

accounted for by domestic consumption for feed, fuel, fiber, or horticulture

was placed in this category. Since the US was a net exporter of primary

agricultural products in 2012 (USDA 2019), this includes land used to

generate those net exports. However, it is unlikely this land area exceeds the

large amounts of land that could not be accounted for in these analyses, such

as those described above. Therefore, these results are likely an

underestimate.

To understand how the United States’ domestic land footprint fits

within a global context, it helps to examine what the total human land

footprint would be if everyone on Earth lived like the average American. To

do this one must first calculate the per capita US footprint in 2012.

According to the US Census Bureau, the mid-year population of the country

in 2012 was approximately 313,914,040 people (US Census Bureau 2013).

Dividing the total domestic land footprint by this value yields a per capita

US footprint of 0.018 km’, or 4.34 acres. Without any other context this

figure may seem small. Setting aside the fact that this is likely an

underestimate, one can provide that context by estimating the global land

footprint if everyone on the planet needed 0.018 km?, on average. The world

population mid-2019 was approximately 7.7 billion (United Nations 2019).

If the average global citizen in 2019 lived like the average American, the

total global footprint would exceed 135 million km’. This is more than all

ice-free land on the entire planet (130.1 million km* — Hooke ef al. 2012).

In other words, if the rest of the world lived like people in the US, there

would be no bioproductive wild lands left anywhere on Earth, and the

current extinction and biodiversity crisis would be vastly worse. In short, the

US land footprint grossly exceeds what would be proportional or

sustainable.

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Fortunately, most of the global population does not live like the

average American, and all ice-free lands are not modified by humans. This

is not to say that the current situation is acceptable. As of more than a decade

ago, 53% of ice-free lands had been modified for human use (Hooke ef al.

2012) and 75% of all global land showed a measurable human impact

(Venter ef al. 2016). As the global human population has grown significantly

since then, the current global land footprint is almost certainly larger. To

make matters worse, within the next three decades, the US population is

projected to grow to 398 million (US Census Bureau 2018) and the global

population is expected to reach 9.5 billion (United Nations 2019), nearly two

billion more than the current population. Every net additional person added

to the population requires more land. Given over a quarter of all species are

currently threatened with extinction, due largely to habitat loss (UCN 2020;

Venter et al. 2006; Pereira et al. 2012), continued habitat destruction to meet

the needs of two billion more people will greatly exacerbate the situation.

Since the US contributes disproportionately to ecosystem losses, it is

essential that Americans identify ways to significantly reduce their footprint.

While there are many actions that can and should be carried out to

accomplish this, the findings of this study show that a single change alone

could eliminate the majority of the US land footprint: drastically reducing

farmed meat consumption (and other animal products). Meat/animal

production land accounts for nearly three quarters (71%) of the total US land

footprint, an area equivalent to 51% of the entire contiguous US. That is an

extraordinarily heavy environmental burden, and one that could be largely

eliminated if alternative protein sources were utilized. It is often assumed

that meat is an essential component of the diet because, unlike most plants,

it is rich in protein. One might further assume that if people eliminate meat

from their diet, they’d either have protein deficient diets, or have to replace

it with large amounts of plant-based protein, which in turn would require

large amounts of land. Not so. When compared to protein rich crops like soy

and peanuts, animals require substantially greater amounts of land to

produce the same amount of protein. Beef is the worst in this regard. It takes

approximately 140 times more land to produce the same amount of protein

as plant-based protein sources such as tofu (Alexander ef al. 2017). Similar

results hold when comparing land needed to produce the same number of

calories compared to a variety of plant products (Eshel ef al. 2014:

Alexander et al. 2017). Not only can substituting plant-based protein in place

Washington Academy of Sciences

of beef save land, it can also significantly reduce other environmental

impacts such as greenhouse gas emissions and improves the nutritional

profile of a diet as well (Eshel et al. 2014, 2016). Other meat sources such

as pork and chicken are not quite as land-intensive as beef due to the

extensive use of highly concentrated factory farming (which has its own set

of ethical and environmental problems — Henning 2011), but even they

require roughly 4-14 times more land to produce the same amount of protein

as plant-based alternatives (Alexander ef a/. 2017).

Based on figures in Table 2, if one assigns all 3,144,847 km? of

grazing land to beef (at least 620,000 km? of which are suitable for crops —

Eshel ef al. 2014) and all cropland for feed to the most land-efficient of the

other meats (requiring only 4 times as much land as vegetable protein), the

elimination of animal production land and replacement of meat with

vegetable protein could eliminate over 2/3 of the total US domestic land

footprint (at least 3.7 million km’). Even if one accepts that some animal

production would remain for food, labor, recreation, entertainment, efc., a

large-scale replacement of meat with plant-based protein could still

eliminate well over half the US domestic land footprint. No other action or

combination of actions, can come even close to this impact.

One common objection to the large land burden of meat is that many

grazing lands are semi-natural and therefore not as heavily modified as

cropland and developed land. While this may be partly true, livestock

nonetheless profoundly alter many of these ecosystems, causing particularly

heavy damage to riparian and stream ecosystems, contributing to soil erosion

and desertification, altering species compositions, reducing primary

productivity, and a host of other deleterious impacts (Fleischner 1994;

Belsky et al. 1999; Krausman et al. 2009). Nevertheless, for the sake of

argument it is possible to provide a more conservative, best case scenario of

the impact of meat production. For this revised calculation, only the

following will be included: cropland for feed (695,064 km* — Table 2),

livestock infrastructure land (82,287 km? — Table 2), Bureau of Land

Management (BLM) land that has been evaluated by BLM staff and found

to significantly degraded by livestock (147,829 km? — USDI 2013), and

grazing on prime, bioproductive land capable of supporting crops, forests,

or other mature ecosystems that would be incompatible with grazing

(620,000 km? — Eshel et al. 2014). The new total of land significantly

Summer 2020

impacted by animal production comes to 1,545,180 km’. Despite the fact

that this is a gross underestimate of livestock’s footprint, it still nearly equals

all other parts of the US domestic land footprint combined (1,588,377 km’).

Thus, no matter how one calculates it, meat/animal production comprises a

massive and largely unnecessary part of the footprint.

Another set of concerns one might raise regarding these findings

relates to the practicality of significantly reducing meat consumption in the

US, and the likely fate of any lands abandoned from animal production.

People who consume meat are unlikely to cease or reduce this consumption

without compelling reasons to do so. The data presented here should be seen

as simply one of the first steps in this process by providing those concerned

about the environment with one more compelling reason to decrease

consumption of these products. How this can be done is as simple as

replacing all or a portion of the meat in one’s diet with protein rich

vegetarian alternatives, including legumes or a growing array of vegetarian

“meats” available in grocery stores and restaurants. As for the fate of lands

no longer needed for animal production, this will likely depend on

ownership and market conditions. Many animal production lands are on

government property. Removing animal production from these lands would

certainly reduce human impact on these lands, and in many cases allow for

the restoration of natural conditions. Where native herbivores and their

predators have been removed or displaced to accommodate livestock, the

return of these species would help further the return to native conditions. As

for private animal production lands, much depends on the desires and

resources of land owners as well as land use demands in the region. In some

cases, these lands would return to natural conditions, much as the

abandonment of agricultural lands in the northeastern US led to forest

regrowth there. Purchasing of some of these lands by governmental or non-

governmental conservation organizations, or offering tax incentives or other

financial incentives for conservation easements would certainly help

increase the probability that these lands will return to natural conditions. In

other areas were development is increasing to accommodate a growing

population, some of these lands may be replaced with development. An

important point to note is that, while this study is very much about reducing

America’s land footprint, a less ambitious goal would simply be to slow the

rate of increase in this footprint. Thus, even if some reductions in animal

productions lands are replaced with development (or another human land

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use), those reductions still yielded important benefits by ensuring existing

native habitats such as forest, grasslands, wetlands, etc. did not have to be

destroyed to meet the growing demands for land to accommodate a growing

human population.

All of the above is not to say that reducing meat/animal production

should be the only focus for decreasing the US land footprint. It is merely

the single best and most significant way of doing so. Ideally, Americans

should examine all land-intensive activities/products and choose alternatives

that are less land-intensive or exert less pressure on native ecosystems. For

example, many areas in the US and abroad are experiencing rapid growth of

poorly planned urban sprawl (Artmann ef al. 2019). Urban sprawl leads to

more rapid habitat loss and fragmentation compared to compact, green cities

(Artmann ef al. 2019). As urbanization is expected to grow significantly in

the coming decades, posing increased threats to biodiversity (McDonald er

al. 2008), pushing municipalities and other governmental bodies to embrace

smart, compact, green growth could help lessen the environmental toll.

Another area of concern is the continued growth of allegedly “green”

forms of food and energy production that actually require more land than

standard modes of production. A prime example of this is conventional

biofuels (corn ethanol and soy biodiesel). These fuels, which use the

equivalent of nearly 3% of contiguous US land area, are extremely

destructive, requiring up to 1000 times more land per unit of energy

generated than nuclear power, and dozens of times more than fossil fuels

(Brook & Bradshaw 2014). They have also been found to drive up food

prices, contribute to food shortages, and increase other environmental

problems such as water pollution (Pimentel er a/. 2009). Since fossil fuels

are typically used at every stage of their production, these biofuels often do

very little to actually reduce overall carbon emissions (Djomo & Ceulemans

2012). Their continued expansion would lead to massive habitat loss,

exacerbating the ongoing biodiversity crisis, and actually result in a net

increase in carbon emissions in some cases (Groom ef al. 2008; McDonald

et al. 2009; Djomo & Ceulemans 2012; Webb & Coates 2012). While food

waste and algae-based biofuels have an extremely low footprint and should

be promoted (Groom ef al. 2008), conventional biofuels (those used in the

US) have an unacceptably high environmental burden and should be

eliminated from the US energy mix.

Summer 2020

ioe)

Other renewables too can have considerably higher land footprints if

not sited properly. Solar, when placed in arrays requiring removal of habitat

or cropland, rather than over existing infrastructure, or wind turbines, when

not placed offshore or over existing human modified landscapes, can also

destroy significantly more habitat than conventional energy sources like

nuclear (Brook & Bradshaw 2014).

A similar situation applies to food production. Cropland for food is

the second largest individual category of land use in the US after

meat/animal production (Table 2). Choices consumers make with respect to

non-meat food sources can have significant impacts on their land footprint.

When it comes to foods touted as “sustainable,” there is tremendous

variability in the extent to which they live up to that moniker. Things such

as vertical and community gardening placed in existing developed

landscapes offer the potential to increase food production with very minimal

to no increase in land footprint. These modes of production should be

encouraged. By contrast, organic agriculture is much more problematic. On

average, organic crops have significantly lower yields than conventional

crops (Seufert et al. 2012; Kravchenko ef al. 2017). Combined with the

additional land typically needed to produce fertilizer (from plant or livestock

sources), organic agriculture often requires 1.5-2 times as much land as

conventional agriculture to produce the same amount of food (Kirchmann ef

al. 2008; Kravchenko ef al. 2017). There are exceptions, however. Yields

for many organic fruits can rival that of conventional modes of production

(Seufert et al. 2012). Where organic crops can achieve sustained yields at

the levels seen in conventional crops, using fertilizers that require little

additional land, such as human waste, organic can offer an excellent

alternative to conventional agriculture. Unfortunately, this is not the case for

most organic systems at present. Until this changes, it is not practical or

sustainable to implement organic agriculture on a large scale. It is not

feasible to feed the existing 7.7 billion people on the planet (800 million of

which are malnourished — FAO ef al. 2018), along with another 3 billion

people projected by the end of the century (United Nations 2019), using

agricultural techniques that require significantly more land. Instead,

scientific and technological advances that increase yields while reducing

pesticide application (e.g., integrated pest management), nutrient runoff, and

land footprint, regardless of arbitrary labels, should be promoted.

Washington Academy of Sciences

o>)

Finally, projected population growth should not be viewed as a fait

acompli. Every additional person added to the planet adds to the overall

human footprint. For too long, many environmentalists have avoided

addressing the serious problem of population growth. National and global

land footprints are already too large, as evidenced by the tremendous number

of species threatened with extinction due to habitat loss (Venter et al. 2006;

Vie et al. 2009; Pereira et al. 2012; Tittensor et al 2014; Grooten & Almond

2018). Increasing these footprints to accommodate more than 3 billion

additional people will be devastating. Aside from reducing meat

consumption, there is perhaps no other change humans could make that

would have a greater impact on habitat loss and biodiversity declines in the

future than ending the continued expansion of the human population.

ACKNOWLEDGEMENTS

I would like to thank Jeremy Gencavage, Logan Hall, and Erin Silva of the

Eastern Shore Regional GIS Cooperative and especially Art Lembo at

Salisbury University for their tremendous assistance in cross-tabulating the

NLUD and NLCD data in ArcGIS. I am also grateful to Sonja Oswalt of the

US Forest Service for helping obtain timber harvest data.

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BIO

Aaron Hogue received his PhD in biology at Northwestern University. He

subsequently went on to complete a postdoctoral fellowship at Duke

University School of Medicine, Department of Biological Anthropology and

Anatomy, prior to arriving at Salisbury University, where he is now an

associate professor in the Department of Biological Sciences. His research

broadly examines the relationship between organisms (particularly

mammals) and their environment, with an increasing focus on the impact of

our own species on terrestrial ecosystems and the species they contain.

Washington Academy of Sciences

Approaches to Fostering Industry-Academic

Collaboration

Joanne M. Horn

J. Horn Bioservices LLC

Abstract

Civil societies today face enormous pressures associated with shrinking

resources relative to continuing population growth and climate change.

In response to these challenges governments and industry can more

effectively fund programs to foster directed and impactful collaborations

between the academic and industrial sectors. The downstream benefits

of these collaborations include reducing research costs, better use of

university research infrastructure, retaining student talent for future

employment, training students in real-world industrial problem-solving,

taking advantage of academic networks, and blue-sky approaches.

While individual States have sponsored these programs, and have been

shown to generate far more revenues than costs, Federal programs can

be implemented that would have far-reaching effects. Grants, Grand

Challenges, small business incentives, contract set-asides, and

fellowship programs are some of the programs that can be executed on

the national level to achieve these ends.

Rationale and Need

SUCCESSFUL COLLABORATIVE INDUSTRY-UNIVERSITY research models

have been shown to have very significant impacts on regional economies.

Virtually all technology hubs in the U.S. are co-located and partly driven by

cooperative work with large research universities (e.g., Boston, MA;

Research Triangle, NC; San Francisco, CA; San Diego, CA). Leveraging the

cutting-edge knowledge, imagination, and reasonable research costs at

partner universities have propelled industries forward, thus creating capital

gains. At the same time these partnerships have created a pipeline of trained

students and academics for downstream employment, opened up new fields

of knowledge, and allowed universities to broaden their programs and

facilities. Academic collaborations not only drive workforce development,

but incentivize students to stay local, thus retaining talent while also

attracting new businesses to the area. Thus, partnerships between

universities and industry can be extremely mutually beneficial. Clearly,

Summer 2020

these types of partnerships have had far-reaching economic and educational

benefits, and further enhances the social mission of universities.

Expanding and capitalizing on these collaborations requires an

understanding of how they are initiated. In Maryland there are a number of

organizations that work with academia-industry partnerships, however most

focus solely on Technology Transfer, a limited option. While large

corporations may undertake a focused study to determine the best

institutions with which to partner, the truth is that most partnerships develop

ad hoc: For example individual researchers know each other through

professional meetings or publications, a Board Member is an alumnus, a

Dean knows someone doing complimentary work at a particular company,

or a company's desire to support a local institution. And while personal

relationships and public support are always important, they are not always

the most effective means of seeking out the best partners. Also, much of our

current economy is being driven by small business and startups which have

few resources to initiate grants or capital funds to universities, but arguably

may benefit the most from having these collaborations. In short there is no

set formula for finding partners, funding, or threading one's way through

negotiations, particularly for small companies.

Potential Federal Models

So what approaches can government use to incentivize the most

productive collaborations between industry and academia? The following

examples provide some approaches:

I. Grants to Public Universities for collaborative projects with industry;

industry finances matching funding

This is a model that was very successful in California when the State funded

$450M ($20M/year) from 1996 to 2007 to Univ. California researchers to

collaborate with industry on projects strategically aimed at benefiting the

California economy. The focus was on early stage basic feasibility work. It

resulted in supporting over 2000 graduate students, allowed companies to

undertake projects they could not perform in-house, created 5000 jobs,

helped startups raise new capital, encouraged faculty to expand their

Washington Academy of Sciences

collaborations with other companies, and resulted in some students starting

their own firms!.

Maryland instituted a similar program called the Maryland Industrial

Partnerships (MIPS), except that the focus was on translational research,

explicitly solving critical problems in product development (so farther

downstream than the UC approach). MIPS has been in place for 30 years

with about $1.5M invested per year ($51M over the lifetime of the program)

with a $100K limit per project. It has more than paid for itself, generating

$166M per year in income and other taxes from the jobs and products

generated’.

These programs have been hugely successful and generated much

more value than they have cost. Therefore, it seems wise to expand these

types of programs to the Federal level. Other components to them might

include a mandatory requirement for educating high school interns, or

incorporating bachelor students into the projects, along with graduate

students and post-doctoral fellows. The programs might be likewise

broadened by incorporating other disciplines, including business or

marketing, design or law to make them multi-disciplinary, reflecting true

business needs.

2. Financing Institutes that Address Grand Challenges

Federal agencies have traditionally funded large independent research

institutes or projects within Universities, including the DOE national labs,

DoD labs (e.g., Lincoln Lab at MIT), and NSF labs and study centers. None

of these institutions, however, has a direct mandate to intentionally and

foundationally involve industries, nor are any directly aimed at propelling

economic development. There have been industries that banded together to

establish institutes, for example GSK, Merck, and Novartis started the

Structural Genomics Consortium to carry out basic research; all results are

placed in the public domain so there are no IP issues. Grand Challenges

attack critical problems across broad areas, result in transformational

change, and create new fields and markets. The Federal government could

Edmonson, G., Valigra, L., Kenward, M., Hudson, R.L. and Belfield, H. 1999.

Making Industry-University Partnerships Work, Science|Business Innovation Board

AISBL, 50 pp.

2 http://www.mips.umd.edu/impact.html

Summer 2020

create Grand Challenge-based institutes that demand the incorporation of

both industries and academia. This would have broad appeal to both sectors;

academia thrives on long term problem- solving, while industries need the

basic questions to be addressed in the context of relevant markets. The

Institutional funding could be based on urgent issues facing the Nation and

our economy, e.g., energy distribution, fisheries restoration, advanced

transportation technologies, global health security, agricultural adaptation to

climate and globalism, CQO2 sequestration and mitigation, novel

infrastructure materials. Moreover, these institutes could transcend

traditional academic and governmental silos, incorporating science,

manufacturing, business, law, and policy to address these problems with a

systems approach.

3. Startup- or small business- focused grants that incentivize working with

academics

Small Business Innovative Research (SBIR) programs do not typically

demand any specific partnering, but some set-aside of those grant funds

could be used to foster collaborations between academia and industry.

Especially for small firms with limited resources these collaborations could

prove a pivotal element to their success. An alternative approach could be to

set aside some of the SBIR funding to work with Federal Labs; this would

avoid the dilemma that Federal labs often encounter to collaborate:

sacrificing their own operating funds to support a small business

collaboration.

4. Government contract research set-asides for industries to work with

universities

Federal agencies often contract large research-directed companies (CROs,

Contract Research Organizations) to carry out sizable, early stage projects.

If contract vehicles included a requirement to work with universities, it

would foster collaborations. This would be particularly amenable for

executing early stage ideas, feasibility studies, or technology integration.

Large government contractors could manage their own competitive proposal

process to work with universities on a given contract. The academic

component could be managed as a subcontract to the primary contractor such

that the FAR requirements could be handled by the prime contractor.

Accountability could be built into the reporting metrics including, number

of students taught, employees placed, Intellectual property generated, efc.

Washington Academy of Sciences

5. Fellowship program to work as part of the graduate degree

The Federal government has trainee fellowships for institutions that fund

graduate students throughout their graduate school career; these are highly

competitive programs that typically fund an entire department of graduate

students. There are also specific niche programs that focus on minority

fellowships, or other targeted sub-populations. However, to our knowledge,

there are no programs that encourage students (and by extension, their

mentors and graduate departments) to spend a semester working within

industry. This affords a chance for both the student and the company to

gauge experience and performance, and it sets the stage for generating a

pipeline of trained employees. The student gets to work on applied problems,

in real teams, and function in a corporate environment with real-world

constraints. This type of program would also encourage faculty to engage

with industry, which could generate larger downstream collaborations. With

fewer than 20% of Ph.D. students able to secure academic positions’, this

shows students what they can expect in industry.

Summary

The Nation and the world face enormous challenges to meet the

needs of population reaching 9.7 billion people by 2050*, along with

changing climate, aging infrastructure, income disparity, and resource

constraints. All challenges, however, also present opportunities to meet

these needs with creative solutions that generate economic value.

Combining the benefits of industry and academic research generates an

engine, using the blue-sky visions of academic license with the market-

driven guardrails of industry. These combinations have been shown to be a

huge driver of creative solutions and wealth. The U.S. government should

encourage these relationships and guide their formation.

3 https://lifesciencenetwork | | .connectedcommunity.org/blogs/leah-

cannon/2016/09/15/how-many-phd-graduates-become-professors

ang ww.un.org/en/development/desa/new s/population/2015-report.htm!

Summer 2020

Bio

Joanne Horn received a Ph.D. from Univ. California Berkeley in

microbiology, where she studied DNA repair and recombination in

Pseudomonas. Dr. Horn spent a post-doctoral fellowship at the German Natl.

Institute for Biotechnology, working on generating bacterial metabolic

pathways for mercury decontamination, and enzymatic fusion proteins.

Following her studies Horn taught at Univ. West Florida, then went worked

at Lawrence Livermore Natl. Laboratory, followed by research and

development in the commercial biotechnology sector. Horn has supervised

global health security projects in Central Asia and Africa as part of a US

Government Defense contract, and directed a State-funded nonprofit aimed

at driving STEM-based industries by partnering with higher education. She

is currently an independent consultant.

Washington Academy of Sciences

RESOLVING THE KICKER’S CONUNDRUM AND THE

PUNTER’S PARADOX

A physics-based equation to rank football kick(ers)

and punt(er)s

Tae. Lipscombe

Catholic University of America

Abstract

In American football kickers attempt to maximize both the distance

travelled by the ball and the hang time. These two objectives, though, are

mutually exclusive, and result in the kicker’s conundrum or the punter’s

paradox: what should the kicker aim for? By means of a simple football

observation we develop a simple expression for the optimal kick in

football. In real life, though, the ideal punt is not likely to happen. Kicking

camps, which young college prospects attend to catch the attention of

coaches, rate kickoffs and punts in terms of a points system based on a

simple formula. This we show leads to a different criterion, which

rewards “Bigfoot” — the player who can kicker the hardest — over the

perfect punter. Young kickers attending the camp should adopt a different

strategy, kick according to the equation, and kick as hard as possible. We

propose an alternative formula, one that rewards range and hang time, but

which punishes violations of the “perfect punt” condition. College

coaches on the lookout for kicking and punting talent might want to think

again about the rankings generated by such kicking camps.

Introduction

THE EQUATIONS FOR PROJECTILE MOTION are well known. These predict

that a ball, launched at an angle @ to the horizontal at a speed v, will land

at a distance (the range) R, given by Equation (1):

aa vy’ sin 20

(1)

This holds when the launch and landing heights are equal, which truly

requires a level playing field. The maximum range, then, occurs when the

launch angle is 45°.

The ball’s time of flight (or hang time), 7, is determined by equation (2):

Summer 2020

a 2vsin 6

This is maximum when the ball is kicked vertically upwards, at an angle

of 90°.

(2)

These equations illustrate the kicker’s conundrum or the punter’s paradox:

The football coach who selects the team and makes the cuts wants both

distance and hang time on the kickoffs and punts — but physics dictates

that you can’t have both’. Above the 45° launch angle, hang time increases

but range decreases. Below 45°, the range will decrease and the time of

flight will decrease. Those who have watched young kickers in action

know full well they tend to kick the ball at a relatively low angle, assuming

this will give them maximum range. It doesn’t — and furthermore, it ruins

their hang time.

To resolve the kicker’s conundrum, we appeal to football. Namely, no

matter how far you kick the ball, no matter how long it hangs in the air,

the coach also wants the receiving team to be unable to return the kick off

or punt. Consider, then, a kickoff. Players on the kicking team (the kick-

off coverage) are sprinting at full speed and, optimally, cross the line from

which the ball is being kicked (the 40-yard line in high school; the 35-yard

line in college; the 25-yard line in the NFL) at the exact moment when the

ball is struck. If they are ahead of that line at the moment of impact, they

are offside. If they are behind that line, they cannot run as far down the

field as they could before the ball is caught by the receiving team.

This ideal kickoff resolves the problem once we assume that the kicking

team all sprint at speed wu. Namely, we want the ball to land at exactly the

moment when the kicker’s team arrives. However, the downfield

component of the ball’s velocity is v cos 8. The perfect punt or the ideal

kick, then, is one whose launch angle is determined by Equation (3):

u=vcosé. (3)

' The kicker’s dilemma, as it was called, was probably first introduced into physics in

Peter Brancazio “The Physics of Kicking a Football”, The Physics Teacher, October

1985, 403-407. He used data from NFL kickers to explore their launch parameters of

angle and velocity.

Washington Academy of Sciences

This simple expression is part of a larger body of work — pursuit curves.”

In essence, we are looking at the pursuit of a parabolic projectile (the ball)

by a pursuer who moves in a straight line at constant speed.

Typical of a pursuit curve, we introduce the velocity of the ball relative to

that of the runner. Namely, define a by Equation (4):

gk (4)

Immediately, we know that a > 1. Otherwise, the ball would always lag

behind the runner. Note also that cos 8 = = This suggests that the faster

the ball is launched, the higher the launch angle can be to allow the kick

coverage to chase it down optimally.

We can calculate the range and the hang time of such a kick off. We know

from Equation (3) that sin @ is given by Equation (5):

sind = ,/1——- =. (5)

(Oce 04

The range is therefore given by Equation (6):

_vsin2@ _2v sinO@cos@ _ 2u” poe (6)

§ S §

Unsurprisingly, this means that the faster the ball is kicked, the farther it

will travel. (Physics also dictates what a kicker can do to strike the ball

more effectively, so that its launch speed is higher.’ And it shows what air

drag can do, and how best to kick when faced with a stiff breeze.* In Ohio

2 A good introduction to pursuit curves, from a physics perspective, is Carl E. Mungan,

“A classic chase problem solved from a physics perspective”, European Journal of

Physics, 26 (2005), 985-990. See also Trevor Davis Lipscombe, The Physics of Rugby,

pages 66-70. (Nottingham: Nottingham University Press, 2009).

3 See Timothy Gay, The Physics of Football, Chapter 5, “Kicking the Football”, pages

129-166. (New York: Harper Collins, 2005).

4 Trevor Davis Lipscombe The Physics of Rugby, Chapter Four, “Kicking, the Habit”,

pages 95-130. (Nottingham: Nottingham University Press, 2009).

Summer 2020

old-fashioned kicking, where the ball is struck with the toe rather than,

soccer style, with the instep, is still common.’)

The hang time, 7, 1s given by Equation (7):

eg a i Sy (7)

§ §

This means that, no matter what the launch speed, there is always a perfect

kick off, one where the ball lands at exactly the time the kickoff coverage

arrives.

There is a natural objection, namely, the ball is in the air and often is caught

by the receiving team, so there is a height difference between launch and

catch. However, at the kicking camps that young college prospects attend,

kickoffs and punts are charted from where the ball is kicked to where it

lands, so the assumption of a horizontal surface is justified in that case.

The above equations, then, are an approximation, and one could instead

use the equations for the range of the ball launched from y = 0 and caught

ball is caught at chest height, about 1.5 meters, the approximation should

work fairly well.

For punting the situation is significantly more complicated. The height

differential is less, as punts are typically kicked at about knee height,

unlike a kickoff, which is from the ground or from a small tee. However,

the coverage starts sprinting the moment the ball is snapped at time t = 0,

and the punter kicks the ball some T seconds later at a distance L behind

the line of scrimmage. This means the ideal punt is one given in Equation

(8):

vy’ sin 20

——————— u(

R ie eds. (8)

> Ben Keslin, “Old Fashioned Place-Kickers Retain a Toehold in Ohio High Schools,”

Wall Street Journal https://www.wsj.com/articles/old-fashioned-placekickers-retaina-

toehold-in-ohio-high-schools- 1379989900 (retrieved June 24, 2020)

° See, for example,

https://www.usna.edu/Users/physics/mungan/ files/documents/Scholarship/Projectile.p

Washington Academy of Sciences

By means of Equations (1) and (2), we can recast this as Equation (9):

ae 2 ‘

v sin 2 au{ SPE eli (9)

i 2

Consider only those punts for which the range, R > L, and which are

kicked quickly, so that tT « T. That is to say, our simpler equation holds

for elite punters who kick the ball a great distance, with a large hang time,

soon after the snap of the ball.

The Kicking Camp Equation

The criterion expressed in Equation (3) for the ideal punt is unlikely to be

achieved in real life. No matter how much a kicker practices, so that the

speed with which they kick the ball is very nearly always the same, and

the launch angle is close to being constant, there will always be some

variation. How, then, can we judge a set of “almost perfect” punts or

kickoffs? Or, perhaps more important, how can we determine the hot

prospects among high school football kickers, ranking them to see who

merits a Division I college scholarship.

One approach of scientific interest is that taken by various kicking camps,

such as those arranged by Kohl’s and Kicking World. In assessing punts

and kickoffs, they award points, P, based on what we call the Kicking

Camp Equation (KCE), Equation (10):

P=ReuT. (10)

Kickers scoring high points at a Kicking World National Showcase, as

given by the KCE, garner attention from special-teams coaches at the

major football colleges (FBS teams, like Clemson, Alabama, and Notre

Dame).

Intriguingly, the KCE, gives a different criterion for kick-off angle than

the “perfect” formula of Equation (3).

Written out in full, using Equations (1) and (2), the KCE awards points

according to Equation (11):

= vy’ sin 26 ” 2uvsin@

ge &

P (11)

Summer 2020

Given a launch speed v, we seek to kick off at an angle that will maximize

points. That is to say, we seek the angle that maximizes the points, a

condition given by Equation (12):

GE ne ee (12)

do Z g&

The angle that maximizes the points as given by the KCE is given by

Equation (13):

acos20+cosé=0, C3)

which can be rewritten as Equation (14)

2acos’ 8+cosd—a=0. (14)

This is the quadratic equation, whose solution is given by Equation (15):

V1-E8ar 1

os = (15)

This differs significantly from the “perfect punt” condition. Namely, given

that punts and kickoffs can go 60 meters, suggesting a launch speed of

about 25 m/s, and that athletes can sprint at 10 m/s, we have a~2. In other

words, we can expect that, to a good approximation, the ideal kicking

world punt is given by Equation (16):

] ] ]

cos 9 = = —-—_+——_=— + .... (16)

YD Aa 323/207

For high launch velocities, this corresponds to a launch angle of 45°.

Hence, the KCE rewards those who kick for maximum range or, to be more

exact, who hit the ball at slightly less than 45°.

Those who kick at 45 degrees receive points given by Equation (17):

p=" (a? +V2a), (17)

whereas those who kick perfectly obtain points given by Equation (18):

Pa eet (18)

Washington Academy of Sciences

The KCE points system, then, rewards “Bigfoot” — the person with the

“Big Foot” who hits the ball hard at 45 degrees, rather than the kicker

whose ball is perfectly synchronized with the coverage. The two points

totals are equal for a = V2 = 1.414... But as most kickers have a higher

launch speed (over 20 m/s, and thus with a > 2) the synchronous kicker

is at a disadvantage.

An Improved Kicking Equation

Though the KCE rewards Bigfoot, this is not optimal’. If the ball

outdistances the coverage, the receiving team can gain many yards before

the coverage arrives and, as the receiver is at top speed, he can be difficult

to tackle. Consequently, we modify the KCE to penalize those who either

over- or under-kick the coverage. That is to say, a ball hit too far should

have been angled more steeply, giving less distance but more hang time.

A ball hit more steeply, so that the coverage in essence have to wait for it,

should have been launched at a shallower angle. Consider the improved

kicking equation (IKE), which is a modification of the KCE, and is defined

by Equation (19):

P=R+uT -[R-uT]. (19)

The farther the kick is from the ideal, the more the kicker is punished. We

can express this differently. Namely, if R > uT, this reduces to 2R, but if

R < uT, it becomes 2uT. In other words the points awarded obey Equation

(20):

P=2min(R,uT). (20)

There are two distances in play. First is the range of the ball. The second

is the distance run by the kicking team coverage. The KCE simply sums

these. The IKE doubles whichever of the two is the smallest. This means

that if you hit for distance and lose hang time, you score twice the distance

your coverage can run during that hang time. If you have a long hang time,

you score only twice the distance of the kick.

7 An objection might be that, with a sufficiently hefty boot, a young player can be

trained to aim for more hang time. Or, rather, that it might be easier to coach a player

who can kick the ball hard to aim for more hang time, than to get a player who punts

perfectly to hick for more yards.

Summer 2020

A punt at 45° degrees, currently the angle most rewarded by the KCE,

generates the following number of points using the IKE, as per Equation

(2);

Ou es : 2D 2 2 2

p= 2min{ S828, 2vsine) ain] SE } 01)

& &

which reduces to Equation (22):

ee Rae (22)

For the perfect punt R = uT which would consequently generate the points

score according to Equation (23):

zeal ah (23)

Again, these two punts are equal for a = V2 = 1.414..., but for alpha

greater than this value, the “perfect punt” scores more points.

Discussion

The KCE and the IKE provide different measures of how good a kick is.

The KCE rewards those who can blast the ball hard at 45 degrees, whereas

the IKE produces a somewhat subtler effect — the punter who can kick 30,

40, or 50 yards and allow the coverage 3, 4, or 5 seconds to get there. This

strategy optimizes the net yardage for the punt, as it means in almost all

circumstances the receiver — with the coverage breathing down his neck —

will opt for a fair catch, with no return.

The question, though, is whether this makes a difference. To do so, we

used the data for punts and kickoffs recorded at Kicking World’s National

Showcase on December 7, 2019.* For these, Kicking World uses two

separate formulas. For punts, the value of w is set at 11 yds/second, which

is a reasonable speed for an elite athlete. For kickoffs, though, a value of

17 yds/second is used. This may seem puzzling, as it is an “equipartition”

https://www.kickingworld.com/camp-result/national-showcase-kickoff-charting-

december-7—2019/ (retrieved June 24, 2020)

Washington Academy of Sciences

principle of sorts. Namely, by multiplying the hang time by 17, you

generate about the same number of yards as the range of the kick. But there

is a good football-related reason behind this. Namely, in college, the ball

is kicked from the kicking team’s 35-yard line. Hence, any kick that goes

more than 65 yards lands in the opponents end zone, permitting them to

start with the ball at their own 25 yard line, equivalent to a 40 yard kick

with no return. The optimal kick off, then, might be one that goes 55 yards,

with the largest hang time possible.

The results are intriguing. For punting, the order remains somewhat the

same. That is to say, if one uses the KCE those ranked (1,2,3,...10) are

ranked 1,2,3,4,5,7,6,9,10,8, which represents a mild shuffling of the top 10

out of the 46 punters whose kicks were charted. The bottom six were

ranked 41,42,...46 by the KCE but are ranked (46,42,38, 43,45,44). So, at

the top and bottom of the pack, there is only a slight rearrangement of the

order.

Kickoffs, though, lead to a substantial reordering. The kickers ranked | to

10 by the KCE now become, with the IKE, ranked (1,3,14,25,7,20,4,

25,17). Of the 56 entrants, the bottom 7 (51—56) as ranked by the KCE

now become (46,48,47,50,55,56). This suggests that the poorer kickers

aren’t affected much by whether one uses the KCE or the IKE, but the top

ranked kickers are. This is, perhaps, not surprising. By using the multiplier

of 17 yds/sec, the KCE rewards hang time significantly more than the IKE.

However, changing the multiplier to 11 yds/second in the KCE does not

change their ranking of kickers significantly.

The major difference in the rankings, then, is mostly due to the punitive

effects of the IKE. Namely, suppose each contestant has two kicks. Kicker

A hits two perfect kickoffs, one long, one short. Kicker B hits one long,

but with no hang time, while the second one is short, but with plenty of

hang time. Kicker B would, as per the KCE, be given the same number of

points as Kicker A, as the two sets of kicks are indistinguishable. However,

Kicker A would far outscore Kicker B by means of the IKE. In fact, Kicker

A might outscore Kicker B with two medium-range perfect punts. Hence,

the IKE rewards consistently good kicking. And consistently good kicking

is probably what most coaches seek.

Summer 2020

Conclusion:

In American football, the kicker’s conundrum is that increasing the range

decreases the hang time, but both of these are highly prized commodities.

By requiring the ball to land at the same moment the kicking team arrives

at the same place, we can determine the optimal launch angle for an ideal

kick. Various kicking camps assess a kicker’s ability according to an

empirical formula. This we show rewards those who can kick the ball hard

and therefore can be far from the perfect punt. We develop a similar

formula, one that simultaneously rewards long ranges, long hang time, but

punishes excesses of either. The new equation might be worthy of

consideration as a means to find talented high-school kickers seeking a

college football career.

Acknowledgment: | thank Peter Lipscombe, whose ability with kickoffs,

punts, and field goals initially suggested this problem.

Bio

Trevor Lipscombe trained as a theoretical physicist and played rugby, a

sport that -- like football -- features kicking and bloodshed. He is the author

of the Physics of Rugby and has been interview by the /rish Times, among

others, for is work on sports-related physics. Trevor works for the Catholic

University of America, whose football team won the Orange Bowl and tied

for the Sun Bowl -- in 1936 and 1940 respectively.

Washington Academy of Sciences

Science Bite — submitted by Paul Arveson

Finally, a Practical Use for 3D Printers!

By the end of March 2020 fear of the pandemic had reached a high level

based on stock market data. Grocery stores were cleared of disinfectants and

paper supplies. Recognizing the vast demand for PPE one of our members

decided to join a small group of local "makers" to fabricate face shields,

masks, and the like using 3D printing technology.

He bought a 3D printer for $210 in early April and had it delivered to the

local "maker space" (WAS has access to such a space at a retail store front).

Working with the manager of the maker space, Abdel Elhamdani, he

gathered several 3D printers and proceeded to fabricate a variety of objects,

including face masks, face shields, and little straps that support surgical

masks behind the head. Working together they produced hundreds of copies

of various designs of PPE. (The NIH has set up a 3D Print Exchange website

to collect codes that can be used to print these designs). They distributed

these to nearby grocers and carry-out shops, as well as to local distribution

points that the local county had set up.

When the supply of PPE for health care workers increased, amateur made

products were no longer accepted by the health care industry. 3D printing is

considered a hobby, not a professional operation. It is difficult to get the

printer settings right, and there are many printing failures. However, one

remaining product is still in high demand. Nurses need the surgical mask

straps, which take stress off their ears from wearing masks all day. So they

printed packs of these little devices and delivered a pack of a hundred of

these to a nearby hospital. They were gratefully accepted.

They donated the printer to the maker space to be used by the creative young

students in the Rockville Science Center in Maryland.

Summer 2020

B :

- aS rt » 7 ™S

=» \ q \ : *

y a *) ne ay a 7 ;

Hj ~~ a ok - ~ ‘ ~4* -.

es ¥ > ‘ell,

Abdel Elhamdani in the maker space

Washington Academy of Sciences

Science Bite — submitted by Ron Hietala

GPS, its current state and current champion (?!)

Who does not marvel at the extent of science and technology in the

Washington, DC area? The innovations that have been accomplished within

50 miles of the Washington Monument would make heads spin, if people

thought about it much.

A favorite example is the Global Positioning System (GPS), developed by a

team at the Naval Research Laboratory led by Roger Easton. It became

functional in 1993. Its original, defining purpose was to enable military

pilots to know their locations without sending out any signals that might

allow anybody else to know their locations. That concept has been

substantially broadened now. Now it is used by drivers to avoid having to

know where they are going, boy scouts to know if they are on the right trail,

runners to know how far they ran, ship captains to avoid being lost at sea,

and other uses too numerous to account.

How much did it cost? If you have to ask, you don’t want to know. $12

billion to get it operational. Much more to refine its accuracy. Still more to

keep it going.

But here is the funny part of this story. Who do you think is the current

champion of global positioning technology? It depends on whom you ask

and which of the many purposes of the system are yours to fulfill.

If you are a farmer in the United States, the answer is obvious; it is the John

Deere Company.

John Deere sells tractors from 20 horsepower to 620 horsepower,

recreational vehicles, and pedal tractors for kids as young as four. Much of

the road equipment you see as you drive using your GPS is John Deere.

Much of the newest equipment used on farms is made by John Deere.

They also sell a global positioning system that has been refined to a

remarkable degree. When the farmer takes the tractor to the field, the

computer on the tractor knows the location of the tractor within two

centimeters. Not kilometers, not meters — centimeters!

The farmer does not even steer the tractor much. The GPS does that, in

combination with the computer. The farmer may drive along the edge of a

Summer 2020

field and give the steering wheel a nudge when it’s about time to turn into

the field and start working, but the tractor does not turn immediately. The

GPS-computer waits until the machine is an exact multiple of the width of

the implement from the edge of the field. There’s no need to waste time and

fuel by misjudging the distance from the edge of the field, not when you

know the location of the tractor within centimeters. If the John Deere-

enabled GPS-computer has run this machine on this field before, it also

follows in the same tracks it made before, even if they were made in earlier

years. This avoids packing additional ground with these machines, which

weigh up to 25 tons. Plants grow better in loose soil. Before GPS, farmers

typically overlapped, about 10 inches, their routes across the field, to ensure

they got the seed, fertilizer and weed chemicals everywhere they were

needed. So now they save some expense on those.

How did John Deere achieve this remarkable accuracy? Most of the errors

made by the global positioning system are related to locality. Errors result

from weather conditions, variations of the location of satellites due to

various gravitational forces as the satellites orbit, the slowing of the signal

due to atmosphere, and the angles at which the signals go through the gas

layers around the earth. Because these errors are relatively consistent within

small distances, they can be reduced if the magnitudes of the errors locally

are known. John Deere maintains stationary GPS stations throughout its

market and broadcasts errors so the farmers’ GPS units can correct for the

errors. Farmers, and anyone else who wants to spend several thousand

dollars, can also buy and maintain their own stationary systems to refine

their location estimates.

All that doesn’t change the history. The fact remains that all the heavy lifting

was done, and the big money spent, by the Naval Research Lab. The U. S.

Navy still maintains the system.

What about the future? The mind boggles. Maybe parents will wire their

children with electronic devices that will send the kids’ precise locations to

the parents. Maybe automobiles will routinely carry their own locations and

the locations of all nearby vehicles in their computers, so they will be able

to roll along the freeways centimeters apart with no fear of collisions. Maybe

airplanes will find their own ways down to the runways and traffic control

towers will be converted into restaurants. There is more to come, we may be

sure; this thing 1s just getting rolling.

Washington Academy of Sciences

Delegates to the Washington Academy of Sciences

Representing Affiliated Scientific Societies

Acoustical Society of America

American/International Association of Dental Research

American Assoc. of Physics Teachers, Chesapeake

Section

American Astronomical Society

American Fisheries Society

American Institute of Aeronautics and Astronautics

American Institute of Mining, Metallurgy & Exploration

American Meteorological Society

American Nuclear Society

American Phytopathological Society

American Society for Cybernetics

American Society for Microbiology

American Society of Civil Engineers

American Society of Mechanical Engineers

American Society of Plant Physiology

Anthropological Society of Washington

ASM International

Association for Women in Science

Association for Computing Machinery

Association for Science, Technology, and Innovation

Association of Information Technology Professionals

Biological Society of Washington

Botanical Society of Washington

Capital Area Food Protection Association

Chemical Society of Washington

District of Columbia Institute of Chemists

Eastern Sociological Society

Electrochemical Society

Entomological Society of Washington

Geological Society of Washington

Historical Society of Washington DC

Human Factors and Ergonomics Society

(continued on next page)

Paul Arveson

J. Terrell Hoffeld

Frank R. Haig, S. J.

Sethanne Howard

Lee Benaka

David W. Brandt

E. Lee Bray

Vacant

Charles Martin

Vacant

Stuart Umpleby

Vacant

Daniel J. Vavrick

Mark Holland

Vacant

Toni Marechaux

Jodi Wesemann

Vacant

F. Douglas

Witherspoon

Vacant

Chris Puttock

Keith Lempel

Vacant

Ronald W.

Mandersheid

Vacant

Jurate Landwehr

Vacant

Gerald Krueger

Washington Academy of Sciences

Delegates to the Washington Academy of Sciences

Representing Affiliated Scientific Societies

(continued from previous page)

Institute of Electrical and Electronics Engineers, Washington

Section

Institute of Food Technologies, Washington DC Section

Institute of Industrial Engineers, National Capital Chapter

International Association for Dental Research, American

Section

International Society for the Systems Sciences

International Society of Automation, Baltimore Washington

Section

Instrument Society of America

Marine Technology Society

Maryland Native Plant Society

Mathematical Association of America, Maryland-District of

Columbia-Virginia Section

Medical Society of the District of Columbia

National Capital Area Skeptics

National Capital Astronomers

National Geographic Society

Optical Society of America, National Capital Section

Pest Science Society of America

Philosophical Society of Washington

Society for Experimental Biology and Medicine

Society of American Foresters, National Capital Society

Society of American Military Engineers, Washington DC

Post

Society of Manufacturing Engineers, Washington DC

Chapter

Society of Mining, Metallurgy, and Exploration, Inc.,

Washington DC Section

Soil and Water Conservation Society, National Capital

Chapter

Technology Transfer Society, Washington Area Chapter

Virginia Native Plant Society, Potowmack Chapter

Washington DC Chapter of the Institute for Operations

Research and the Management Sciences (WINFORMS)

Washington Evolutionary Systems Society

Washington History of Science Club

Washington Paint Technology Group

Washington Society of Engineers

Washington Society for the History of Medicine

Washington Statistical Society

World Future Society, National Capital Region Chapter

Richard Hill

Taylor Wallace

Neal F. Schmeidler

Christopher Fox

Vacant

Richard

Sommerfield

Hank Hegner

Jake Sobin

Vacant

John Hamman

Julian Craig

Vacant

Jay H. Miller

Vacant

Jim Heaney

Vacant

Larry S. Millstein

Vacant

Marilyn Buford

Vacant

E. Lee Bray

Erika Larsen

Richard Leshuk

Alan Ford

Meagan Pitluck-

Schmitt

Vacant

Albert G. Gluckman

Vacant

Alvin Reiner

Alain Touwaide

Michael P. Cohen

Jim Honig