This document discusses using digestible energy instead of total digestible nutrients (TDN) to evaluate feeds. It presents formulas to calculate TDN from digestion trial data and to calculate theoretical digestible energy. While digestible energy alone would not be useful, the document shows digestible energy can be converted to an equivalent TDN value using factors for organic matter content and ether extract levels. This allows TDN to be determined via bomb calorimetry rather than multiple chemical analyses, improving accuracy of feed energy evaluations.

1. G. P. Lofgreen
Feeds
The Use of Digestible Energy in the Evaluation of
1951, 10:344-351.J ANIM SCI
/344
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2. THE USE OF DIGESTIBLE ENERGY IN THE EVALUATION
OF FEEDS
G. P. LOFGREEN1
University of California
THE Morrison feeding standards, which are undoubtedly the most
widely used standards in the United States, are based upon total
digestible nutrients (TDN) as a measure of the energy requirements
of animals and the energy value of feeds. The term TDN is only an
approximate measure of the food energy available to the animal after
the digestion losses have been deducted. Morrison (1948) and others
(Forbes, et al., 1943; Kleiber, et al., 1945; Maynard, 1947 and Mitchell,
1942) have discussed the advantages and disadvantages of this system
in comparison to other expressions of the energy value of feeds. It is
not the purpose of this paper to discuss these various methods nor to
attempt to suggest which should be used. Since the TDN system has
been so widely accepted and because of the difficulty of a rapid and
complete change to another system it seems desirable to attempt to
improve the method now used and to obtain more information as to
its application. Experiments are often conducted in which it is necessary
or desirable to determine the TDN content of feeds or rations. Any
procedure which would facilitate such a determination or increase its
accuracy would prove valuable.
One of the main criticisms of the determination of TI)N is the number
of chemical analyses required and the inaccuracy of some of the methods.
There are a number of objections to the usual scheme of routine feed
analysis commonly employed in the determination of TDN, especially
in the methods of determining the carbohydrate portion. It seems,
therefore, that it would be a major improvement if some method could
be devised to determine TDN which would not involve the determination
of these various constituents.
Maynard (1947) states that some of the uncertainties of the measure-
ment of TDN could be overcome by measuring digestible energy. The
mere measurement of digestible energy, however, without the establish-
ment of its relationship to the TDN content of the feeds would be of
little value since the standards according to which animals are fed most
tThe author wishes to thank H. R. Guilbert and H. Goss for allowing him to use the samples
f~r the digestion trials conducted by them.
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3. EVALUATION OF FEEDS 345
widely are in terms of TDN. For example, in digestion trials reported
by Forbes, et al. (1940) the TDN content of alfalfa-molasses silage
averaged 20.1 percent while the digestible energy was 59.9 percent.
The TDN expressed on the dry basis amounted to 67.6 percent. The
relationship between 20.1 or 67.6 percent TDN and 59.9 percent
digestible energy must be clarified before the digestible energy deter-
mination would be of much value in evaluating the silage according to
our present methods.
The calculation of the percent TDN from the data obtained in
digestion trials can be represented as follows:
(DCP) + (DCF) + (DNFE) + (DEE X 2.25)
(1) TDN ~ 100 X (CP) + (CF) + (NFE) + (EE) + (ash) + (moisture)
where CP, CF, NFE and EE represent the total amounts and DCP,
DCF, DNFE and DEE the digestible amounts of crude protein, crude
fiber, nitrogen free extract and ether extract in the feed.
Similarly the percent of digestible energy (DE) can be represented as:
energy .2- energy _31_ energy _3i_ energy
in DCP l in DCF in DNFE in DEE
(2) DE~ 100 X
energy energy-I- energy energy --l- energy--1-energy/n
in CP ~ in CF -- in NFE ~ in EE ~ in ash -- moisture
From the data presented in table 1 it is possible to calculate the TDN
content of a sample of alfalfa hay by the use of formula (1) :
8.6 + 12.7+ 30.8+ (0.6 x 2.25)
TDN ~ 100 X = 53.5
13.0+ 26.0+ 41.2 + 1.8 + 9.9 + 8.1
By use of average heats of combustion values for proteins, carbohy-
drates and fats it is possible to calculate the theoretical digestibility of
energy according to formula (2):
48.6 + 54.0+ 127.8+ 5.6
DE=10OX 73.4+ 110.5+ 171.0+ 16.9+0+0 _63.5
In the latter calculation the 9.9 grams of ash and 8.1 grams of water
have no energy value with the result that the 63.5 percent digestible
energy is not affected by the amount of water and ash in the feed while
the 53.5 percent TDN would be. Digestible energy, therefore, is
affected only by the organic matter content of the feed. In order to
place the 63.5 percent digestible energy on the same basis as the 53.5
percent TDN, i.e., relate it to the total feed, the 63.5 percent digestible
energy must be multiplied by the percentage of organic matter of the
feed. In the above example the alfalfa hay contained 82 percent organic
matter. The adjustment would therefore be 63.5• 82 =52.1. When
10o
related to the total feed the digestible energy is thus not far different
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4. 346 G.P. LOFGREN
from the TDN, the two values being 52.1 and 53.5 percent respectively.
A careful consideration of the relationship reveals another adjustment
which must be made in order to express digestible energy on the same
basis as TDN. In the determination of digestible energy heats of com-
bustion are determined on the feeds and feces and the energy digested
is obtained by difference. Since the bomb calorimeter automatically
TABLE 1. THE DIGESTIBLE NUTRIENTS AND THEORETICAL
DIGESTIBLE ENERGY OBTAINED IN A DIGESTION
TRIAL ON ALFALFA HAY
Nitrogen
Crude Crude free Ether
Item protein fiber extract extract Ash Moisture
Nutrient content
per 100 grams of
feed, grams 13.0 26.0 41.2 1.8 9.9 8.1
Heat of Combus-
tion, Kilocalories
per gram1 5.65 4.25 4.15 9.40 0 0
Energy consumed
per 100 grams of
feed, Kilocalories 73.4 110.5 171.0 16.9 0 0
Nutrients digested
per 100 grams of
feed, grams 8.6 12.7 30.8 0.6 - -
Energy digested
per 100 grams of
feed, Kilocalories 48.6 54.0 127.8 5.6 - -
XThe figures 5.65 for protein, 4.15 for nitrogen free extract, and 9.40 for ether extract are
average heats of combustion values reported by Atwater (1899) for proteins, carbohydrates and
fats in.a mixture of foods.The value of 4.25 is the heat of combustion of cellulose.
gives the various constituents their proper energy value, the fat in the
total feed consumed as well as that in the digested portion is given a
value of approximately 2.25 times that of the carbohydrate portion.
This is not true in the case of the calculation of TDN where only the
digested fat is given the extra value while the fat in the feed consumed
is given the same value as carbohydrates and proteins. This would
result in a discrepancy between digestible energy and TDN which
would increase as the fat content of the ration increased. In the example
in table 1 the alfalfa hay contained 1.8 percent ether extract. This
would amount to 2.2 percent of the organic matter. In the determination
of digestible energy the bomb calorimeter would give the 2.2 percent
ether extract a value of approximately 2.25)<2.2 or 4.9. This results in
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5. EVALUATION OF FEEDS 347
a value of 4.9--2.2 or 2.7 more than it would have received had it been
given the same value as carbohydrate. If this same thing had been done
in the calculation of TDN it would have resulted in the sum of the
digestible nutrients, with the fat multiplied by 2.25, being divided by
a value greater than 100 (see formula 1). Therefore, in order to express
digestible energy on the same basis as TDN the digestible energy value
previously adjusted to the basis of the total feed must be multiplied by
102.7
the ratio 102.7 thus: 52.1 X -~-53.5. The digestible energy
100 100
and the TDN when expressed on the same basis are now equal. Theo-
retically, therefore, it appears that it is possible to calculate a value
equivalent to TDN by use of the bomb calorimeter rather than the
determination of the complete proximate composition of the feeds and
feces. Such a determination could be made according to the following
procedure:
1. Determine moisture, ash, ether extract and energy on the feed.
2. Determine moisture and energy on the feces.
3. Calculate the percent of the gross energy which is digested.
4. Calculate the conversion factor by the formula:
OM 100 2r (EE X 2.25) -- EE
(3) F = "~6 X 100
where OM represents the percent organic matter in the feed and EE repre-
sents the percent ether extract in the organic matter.
5. Multiply the percent digestible energy by the conversion factor, F.
In the conventional method of determining TDN from a digestion
trial using one feed and four animals it would be necessary to determine
a complete proximate analysis on at least five samples in duplicate.
This would amount to ten determinations of moisture, ash, nitrogen,
ether extract and crude fiber. From the same trials the TDN value of
the feed could be calculated by the calorimetric method from ten
determinations of moisture and energy and two of ether extract and ash
since these latter two constituents need be determined only on the feed.
The TDN value calculated by the calorimetric method would be more
accurate as a measure of the energy value of the feed than the TDN
content determined by the conventional method because the bomb
calorimeter would give the various nutrients their proper heat of com-
bustion values. In the conventional method one has to assume that
all the proteins and carbohydrates in all feeds are of equal value and
that all_fats have an energy value of 2.25 times that of carbohydrates
and proteins. Such assumptions may result in improper evaluation of
a feed or ration.
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6. 348 G. I'. LOFGREN
Because of the possibility of great savings in time and in the number
of chemical analyses and the promise of increased accuracy the sug-
gested procedure has been investigated and compared with the con-
ventional method for the determination of TDN.
TABLE 2. COMPARISON OF TOTAl. DIGESTIBLE NUTRIENTS OBTAINED
BY TttE CONVENTIONAL METHOD WITH VALUES
CALCULATED FROM DIGESTIBLE ENERGY
TDN Value of Ration (as fed)
Ration Conventional Calorimetric
Method Method
percent percent
56.6 57.9
55.6 57.0
Alfalfa Hay 55.2 57.3
53.5 56.0
16.4 16.2
Alfalfa Hay 16.0 15.6
Wet Beet Pulp 16.2 15.9
16.4 16.1
14.8 14.2
Alfalfa Hay 15.1 14.5
Wet Beet Pulp 15.2 14.4
Molasses 15.0 14.4
34.5 40.8
39.9 40.5
Flax Hulls 35.7 33.0
33.9 40.5
56.7 53.8
Various proportions of 57.3 55.0
Oat Hay, Barley, Oats, 56.3 54.3
Dried Beet Pulp, Cotton- 55.3 53.3
seed meal, Limestone 55.2 52.1
and salt 57.1 54.2
51.6 48.4
Experimental
The TDN content of the feeds used in 23 digestion trials was deter-
mined by the conventional method. By applying the conversion factor
calculated by use of formula (3) digestible energy has been related to
the TDN content. Guilbert, Miller and Goss (1947) using sheep as the
experimental animals conducted four digestion trials on alfalfa hay
alone, four on alfalfa hay and wet beet pulp and four on alfalfa hay, wet
beet pulp and molasses. Feed and feces samples from these trials have
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7. EVALUATION OF FEEDS 349
been used in the present study. Four trials on flax hulls have been
conducted with sheep by Guilbert and GoEs (1944) and samples from
these trials were also used in the comparisons presented herein. Seven
additional trials have been conducted using beef bulls on rations con-
sisting of oat hay and various proportions of oats, barley, dried beet
pulp, cottonseed meal, limestone and salt. Chemical analyses were made
according to the methods of the Association of Official Agricultural
Chemists (1945). Gross energy determinations were made by use of a
bomb calorimeter.
Results and Discussion
The TDN content of the feeds used in the 23 trials as determined
by the conventional method and the TDN values calculated by the
calorimetric method are presented in table 2.
Using the paired data system of analysis no significant difference
was found between the two methods. Most of the differences which do
occur are as small as or smaller than the differences between animals on
the same ration.
These data indicate that a great saving in time and chemical analyses
can be made by calculating the TDN value of feeds from the digestible
energy. Where consistent small differences do appear in the values
determined by the two methods those determined from digestible energy
should be more representative of the true energy value of the feed since
no assumptions need be made as to the relative value of the various
nutrients as is done in the conventional method. The relatively good
agreement between the two sets of values is reassuring, however, that
the assumptions made in the determination of TDN by the conven-
tional method may not lead to serious errors in most cases.
When the TDN value is determined from digestible energy by the
proposed method it is unnecessary to determine separate coefficients of
digestibility for the proximate principles. Even though this is a distinct
advantage in the determination of TDN it does not allow one to
evaluate similar feeds by applying average digestion coefficients to the
determined proximate composition. Schneider, et al. (1950) have shown
that the application of average digestion coefficients to the determined
proximate principles results in a better estimate of the nutritive value
of a feed than the direct use of an average value for TDN content.
Even though the proposed method for the determination of the TDN
value of feeds may have the disadvantage of not supplying coefficients
of digestibility of all the proximate principles it should prove especially
useful in experimental work where the TI)N values of feeds and rations
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8. 350 G.P. LOFGREN
actually must be determined rather than estimated from tables of
average digestion coefficients. Of course, one would usually desire to
determine the digestible protein content in either case.
Brody (1935) has suggested that the TDN content of a feed be
estimated from digestible energy by assuming that one pound of TDN
is equal to 1814 kilocalories. Such a factor has the disadvantage of being
only an average value and could lead to erroneous results when applied
to different individual feeds or mixtures of feeds. For example, in the
five feeds or feed combinations listed in table 2 the amount of digestible
energy equal to one pound of TDN varies from 2057 to 2457 kilo-
calories. The use of the factor 1814 in the case of these feeds would
result in a large error as would any average factor. One of the advantages
of the method proposed in this paper for calculating the TDN value of
feeds from digestible energy is that the conversion factor calculated
according to equation 3 is specific for each feed or combination of feeds.
One of the objections to a change from the TDN system of evaluating
feeds has been that the great body of data which has been compiled on
digestion coefficients of the proximate constituents would no longer be
of much value. Because of the close relationship of TDN to digestible
energy it would, however, be possible to calculate from these data the
approximate percentage of gross energy which would be digested by
merely dividing the percent TDN by the proposed factor (F in equa-
tion 3). To evaluate a sample of feed, therefore, one need merely to
determine its heat of combustion and apply the energy digestion
coefficient calculated from the average TDN of a similar feed in the
tables of composition to arrive at an estimate of the amount of energy
which would be digested. For example, the factor for alfalfa hay, all
analyses, given in Morrison's (1948) tables of feed composition would
be 0.848. By applying this factor to 50.3 percent TDN an approximate
digestion coefficient of 59.3 percent for energy would be obtained. This
coefficient could then be applied to the heat of combustion of an alfalfa
hay sample to estimate its content of digestible energy. Such a pro-
cedure would make it possible to use this body of digestibility data if
the digestible energy system were used to evaluate feeds rather than
the system based upon TDN.
Summary
A method is presented by which it is possible to calculate a value
closely approximating the total digestible nutrient content of feeds and
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9. EVALUATION OF FEEDS 351
rations from digestible energy. The method provides for a saving in
time and in the number of chemical analyses which need be made.
It is pointed out that the use of the calorimetric method results in a
more accurate estimate of the energy value of a feed or ration than the
conventional method of determining total digestible nutrients.
Literature Cited
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Atwater, W. O. 1899. Discussion of the terms digestibility, availability, and fuel
value. 12th An. Rep. Storrs Agr. Exp. Sta. pp. 59-110.
Brody, S. 1935. Report of the conference on energy metabolism. National Re-
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Forbes, E. B., J. W. Bratzler and C. E. French. 1940. The utilization of certain
feeding stuffs by cattle. Penn. Agr. Exp. Sta. Bul. 391, 14 pp.
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