OXYGEN POWER

*By Jack Daniels, Jimmy Gilbert, 1979*

Appendix A

Running is
primarily a __conditioning__ sport. It is not a __skill__ sport as is
basketball or handball or, to a certain extent, swimming where technique is of
primary importance. Most of us are able to run without special training, and
for all practical purposes, all of us who do run, do so with nearly equal
efficiency regardless of how “inefficient we may appear or feel. Granted, small
differences in style, technique or “efficiency might spell the difference
between two otherwise equal competitors, but the fact remains that we all
expend about the same relative energy to run at any given velocity which is
within our aerobic capacity (a term which will be described later). Quite
different is the case of swimming or cross-country skiing, where technique
greatly affects the effort we put into any particular speed of movement. For
example, a world-class swimmer could easily cruise through an 8:00 400-meter
swim with relative ease. A poor swimmer on the other hand, might work at
maximum effort just to complete the 400, maybe not even beating the 8:00
barrier. Not only would the poorer swimmer’s total energy expenditure be
greater, but so also would the energy cost per distance covered be greater.

In running
this is not the case. A great runner can run an 8:00 mile very easily whereas a
beginner or less-talented person might be working much harder to run that fast.
However, the __total__ energy expenditure for the mile run would be about
the same for each runner; even the per-second oxygen consumption (a measure of
energy expended) could be identical for both. The difference between the better runner and the not-so-good runner would be in the
__maximum__ rate of oxygen consumption which could be reached by each; the
better athlete would be able to go faster because of a better maximum rate of
energy expenditure being available. What this boils down to is that there is
quite a predictable relationship between running velocity and the energy
demands of running (which can be measured and expressed in a volume of oxygen
consumed per minute). A 4:00 miler and a 6:00 miler might run side by side at
an 8:00 mile pace and both be consuming the same
amount of oxygen per minute (relative to their individual body weights of
course). The difference would be that the 6:00 miler would be working at a
greater percentage of maximum than would be the 4:00 miler; this difference in
maximum oxygen consumption or aerobic capacity (VO_{2} max) is what
makes the difference in their race ability. Figure 1 shows the relationship
which exists between running velocity (expressed in meters per minute) and oxygen
consumption (expressed in ml per kg body weight per minute).

In many sports,
mainly skill or strength sports, body structure or anatomical design are very
important, and it is easy to see that an Olympic gymnast would probably never
become a world-class shot putter because of limited size. Similarly, few people
would expect a 7-foot basketball player to ever become an Olympic gymnast or a
winning jockey. Rules even provide for structural differences by designating
weight classes in some combat sports such as boxing and wrestling. In this case
we are admitting that genetic differences give some people an advantage over
others, even if all are equally motivated and trained.

Not so easy
to accept is the fact that all humans inherit a potential for performance in
sports of a non-skill nature also. We all have a set of physiological features
or attributes which determine our potential for performing such things as the
1-mile run or the marathon. Outwardly two people may look exactly alike, but
may be as different in endurance potential as are a 4-foot 10-inch person and
6-foot 8-inch person different in their ability to perform gymnastics or throw
the discus.

If we
accept the fact that each person has a maximum potential for endurance running
and if we accept the fact that the energy demands of running are quite similar
for all people (as shown in Figure 1), then the main physiological feature
which separates one athlete from another in distance-running ability is the transportation
and utilization of oxygen by the running muscles. This is, in fact, the case.
As mentioned above, this attribute is referred to as aerobic capacity or
maximum oxygen consumption (VO_{2} max).

Of course,
some people are more motivated than others and some reach more of their
potential than others, but the fact remains that a potential c1oes exist and
for each individual there also exists a describable and quite predictable
relationship between running velocity and oxygen consumption.

Over the
years we have had the opportunity to measure both the oxygen demands of many
runners during various velocities of running and the aerobic capacity of these
runners. Using these two sets of values and knowing the best performances for
the runners at different competitive distances has allowed us to accomplish two
things. First, we have developed a regression equation relating VO_{2}
with running velocity (see Figure 1), and second, we have defined a curve, and
accompanying regression equation, which describes what percent of an
individual’s aerobic capacity the individual

is
capable of working at for how long (Figure 2). For example, a person runs at a
velocity which demands about 100% aerobic capacity for about 8 - 10 minutes.
This means that someone who races _{2}
max for _{2} max
for __time__ related,
not __distance__ related. Another way of looking at it is that two runners
of different ability both can run as hard as they can for about 9 minutes; one
might make _{2}
max.

With the
two regression equations presented in Figures 1 and 2 and with the aid of the
mathematical techniques described in Appendix B, the tables in this book have
been produced, What these tables accomplish is to relate performances over various
distances with a reference value, which is also a rough estimate of the V0_{2}
max which would allow the related performances to be accomplished. It is not
necessary to worry about comparing these VO_{2} values with those which
might be measured in a laboratory test because differences in efficiency of
oxygen utilization will cause discrepencies between
the two values. The point is that if an individual’s VO_{2} max is
under or over-estimated it doesn’t matter because that individual’s performance
capabilities will still be related to each other accurately. In fact, the
reference VO_{2} max can be used just as a number for reference
purposes only, to compare values from one table to another.

There are
several very useful purposes for these tables. One is to compare world records
for relative merit. It should be kept in wind that these tables were generated
without reference to records and the fact that world records, even by different
people, relate to very similar reference values supports the physiological
importance of VO_{2} max and the oxygen demands of running in endurance
events. As an illustration, examine the various times which are related to a VO_{2}
max reference of 80.5. We find the following: 3:49.9--mile, 8:l1.5--

Examination
of the current world records shows the 3000, 5000 and 10,000 to be the best;
the record times of 7:32.1, 13:08.4 and 27:22.5 all relate to a reference of
81.1 which is slightly better than the 80.9 VO_{2} max which is related
to the mile and 1500 world records of 3:49.0 and 3:32.1, respectively. The
weakest distance record is the 1:31:31 30Km, but again, the reasons for this
have been stated above.

A glance at
various women’s times shows some interesting findings. The women’s record 1500 is 3:56.0; the 3000 is 8:27.1. These relate to reference VO_{2}
values of 71.4 and 71.1, respectively, and are obviously nearly identical
performances. However, the Women’s current marathon best is 2:27:33, a
performance which is somewhat inferior to what might be expected based on the 1500
and 3000 records and their related V0_{2} maxes. This implies several
things: (1) The best women have not yet become very
involved in marathoning because they are world-class
in more attractive, somewhat less demanding, and more widely available distance
events. Therefore, marathon running is left more open for women whose main
interest is marathon running, which may not yet include very many of the best
physiological specimens. (2) Women are not better distance runners as we
sometimes hear. The women’s records for 1500 and 3000 are both about 11.5%
slower than the corresponding men’s records for these events. In the marathon
on the other hand the women’s record is over 14% slower than the mens; the longer the distance, the greater the difference.
However, (3) based on our earlier findings that at any submaximal
running velocity, women demand the same oxygen consumption as do men, it can be
predicted that women’s times in the marathon will come down to the low 2 hour-20s
before a noticeable improvement takes place in men’s marathon times. A 2-hour
23 minute time would put the women at the same 11+% slower that they exhibit in
the shorter distance events. (4) Of interest is that the V0_{2} max
reference differences between men’s and women’s world record 1500 and __best men__ and __best women__ endurance athletes when tested in the
laboratory. (5) Women with high V0_{2} reference values can expect to
outperform other people who have lesser values, whether they are men or women,
at any of the distances for which they choose to train. In other words, these
tables do not descriminate in any way; they apply
equally to all ages and either sex.

It is
important to understand that during growth the relationship between V0_{2}
and running velocity is constantly changing. This means that a youngster 12
years old who runs a 5:00 mile is also probably capable of a 10:43 _{2} is quite
probably an underestimation of the individual’s true V0_{2} max. This
is because until growth ends the energy demands of running are gradually
getting less and less; an 8-year old requires relatively more energy to run an
8:00 mile pace than does a 12-year old. The 12-year old would probably use more
oxygen per kilogram body weight to run at that pace than would an adult,
however. In fact, this improvement in “efficiency” with growth accounts for a
great deal of the improvement in race times as youngsters
age.

Upon
examination of your own best times for various distances listed in these tables
you may find all your performances to be quite similar. If, on the other band,
you find that the longer distances relate to lower reference V0_{2}
values you are either better suited, genetically, for shorter distances or your
training has been geared for better performances at the shorter distances (or
you may just have a better attitude toward running the shorter races). Chances
are, however, that by concentrating your training more for the longer events
your longer distance times will come in line with what the tables indicate they
should be. Of course, the opposite can also be true--your longer distance times
may be relatively better than you can race for shorter runs. This, again,
reflects either a better genetic endowment for longer races, more interest in
longer races or training geared for longer races. Naturally, we are not all
suited for equal performances at all distances; the world record holder at

The potential
of these performance tables to predict race times brings up another use for the
tables, handicapping. You don’t have to have a time for every runner entered in
a race you plan, to handicap. If you have one or more times
at any distance you can do a respectable job of predicting that individual’s
performance for the race about to be run. If you plan to have a handicap
10,000, use times for 3000 or 15km or _{2} should be the one used in each case, unless
of course the course is known to be inaccurately measured. It is always fun to
try to beat the time your best reference V0_{2 }predicts for you. Using
best-predicted reference V0_{2} values for grouping runners in large
fields is also a possibility. For example, let’s say you are planning a 15km
race and the course won’t allow a real good start for everyone, so you decide
to put the better runners on the front line and slower ones behind. The trouble
is you probably don’t have 15km times on more than a handful of the entrants.
The solution is simple, just place the people with the
best reference V0_{2}s (based on any distance race run) up front and
work back. You could even group athletes by V0_{2}, all over

A final use
of the tables that we will deal with here relates to the matter of improving
performance. Most research indicates that V0_{2} max (expressed in
absolute values--either liters per minute or milliliters per minute) can be improved by about 20% with
proper training. Moderate-to-easy training (as little as 3 to _{2}
max.

__Absolute__ V0_{2} max is a person’s
relative V0_{2} max (expressed in ml per Kg body weight per minute)
multiplied by the person’s weight (expressed in kilograms). The reference V0_{2}s in the tables express aerobic
capacity in relative terms--ml/Kg per minute. To find your absolute V0_{2}
max look up your best performance (the one which
relates to the highest reference V0_{2}) and multiply that by your body
weight in kilograms (weight in pounds multiplied by .454). For example, let’s
say you weigh _{2} (relative) of 53.9 ml/Kg per min. Your absolute V0_{2}
max would then be 53.9 ml/Kg per min X _{2} max
(absolute) another 10%, to 3365 ml/min (1.10 X 3059). If you do in fact realize
that much improvement and your weight stays the same (_{2} max would be 3365/56.75 = 59.3 al/Kg per min
(the same 10% improvement over your original 53.9). This improved reference V0_{2}
(59.3) relates to a 10,000 of 35:43, a 3 minute improvement. Now let’s say you
are also a little over weight and in addition to improving your absolute V0_{2}
max by 10% with training, you also lose _{2} max is
flow 3365 al/min divided by _{2} of 63.4 relates to a
33:43.8 10,000, another 2 minutes faster and a full 5 minutes better than your
original time of 38:46. All this is due to a 10% improvement in absolute V0_{2}
max. The importance of eliminating excess body fat becomes obvious, but a
person should be careful not to lose so much weight that a loss in muscle also
occurs. This would lead to a decrease in absolute V0_{2} max also,
which in effect is detraining aerobic capacity.

It is hoped
that this description of how performance relates to V0_{2} and how
performance is improved, as well as a presentation of the tables themselves
will prove useful to you in analyzing your limitations and potentials.

Appendix B

Procedure
used in arriving at performance times based on oxygen demands of running and
maximum aerobic capacity (V0_{2} max).

The idea
behind the prediction process is as follows. An individual has, at a given
time, an aerobic capacity which peaks at some maximum (V0_{2} max).
Because the individual doesn’t perform at exactly 100% of that maximum value
except in a few specialized cases, knowledge of the effects of anaerobic
capacity, as well as fatigue on the percent of aerobic work capacity used (%V0_{2}
max), can be applied to the situation in order that a reasonable estimate of
the individual’s maximum can be determined for any situation.

It’s well
known that the anaerobic contribution to work is fairly limited, but it does
allow an individual to run at a speed in excess of the speed at which he or she
could run using only aerobic mechanisms.

The
equation for %V0_{2} max, which is used to determine the percentage of
maximum aerobic work capacity used, is reflective of the short term anaerobic
effects as well as the longer term fatigue on the aerobic component. This %V0_{2}
max equation is completely dependent upon time, not distance run, and it
reflects that the longer you run, the lower the %V0_{2} max you can
maintain. Obviously, the % V0_{2} max/time relationship is an integral
part of the equations describing the performance tables developed herein.

The second
component in the development of the performance tables regards the oxygen
demands of running at any given velocity or speed. The relationship (equation)
of speed and rate of oxygen consumption is used to determine the speed at which
a distance can be run for the oxygen demanded. Then using the computed rate of
speed the time required to run the distance is determined. Recall that the % V0_{2}
max is also dependent upon time (the longer the time, the lower the % of V0_{2}
max you can use) so time needs to be inserted into the %V0_{2} max
equation to compute an adjusted oxygen consumption rate, which is in turn used
to compute a new performance level (speed). This new speed again modifies the
time required to run the distance. The new time further affects the %V0_{2}
max/time relationship and so on. This is an example of what is referred to as a
non-linear relationship and the solution techniques for such problems are well
known. The simplest way to solve non-linear equations is to “guess” an answer,
and insert the “guess” in the equations to compute a new answer. Based on the
nature of the resulting new answer, a modified “guess” can be formulated and
inserted in the equations. The process of formulating a new “guess” from the
previous answer is continued until the “guess” used equals the answer obtained
from the equations. Computers make such tedious tasks inconsequential so are
frequently used for this purpose. However, it may be required that several
iterations through the equations are necessary for the answer and “guess” to
converge on a single value. Potentially, this uses a lot of computer time. Another
scheme, called the Newton-Raphson process, is much
more rapidly convergent than the above method, and involves the time rate of
changes (calculus derivatives) of the equations. With a reasonable guess
(within ± 5 percent), Newton-Raphson will converge
with one pass through the equations so the computing process is more efficient.

In
generating the performance tables contained herein, each time for distance
entry was computed by using as a “guess” input, the answer (time) for that
distance from the previous VDOT (V0_{2} max) table value. For example,
in computing the estimate for the mile for a VDOT of 60.5, the “guess” used was
the mile time for VDOT = 60.4, or 4:55.4. This time, 4:55.4,
is input to the Newton—Raphson scheme with an answer
computed corresponding to a VDOT of 60.5 and the result is 4:55.0. Were this
output time of 4:55.0 reinserted in the equations keeping the VDOT value of 60.5
the same, the same answer, 4:55.0, would result meaning the solution has
converged. But if a VDOT value of 60.6 were used, an output time reflective of
that oxygen consumption would result. Incidentally, the “guess” used for the
mile entry is not used for the two mile or other distance “guesses”. All
distances are kept separate, thus rapid solution convergence is assured.

By making
allowances for the short term effects of anaerobic power and fatigue on the
aerobic capacity, representative predictions of performances at various
distances can be made. This is because V0_{2} max is used as a
reference and calculus techniques utilized to accommodate the off maximal
situations. Hence, a relatively good idea of an individual’s VDOT and his or
her potential to run six miles (or whatever distance) can be determined from a
three mile time (or any other distance time for that matter), assuming the
conditions don’t drastically change from one situation to the next, and
assuming training is adequate for both distances.