RP118

CORRECTING ENGINE TESTS FOR HUMIDITY

By Donald B. Brooks

ABSTRACT
Data obtained on a 6-cylinder automobile engine indicate a loss of engine power
with increasing humidity proportional to the volumetric loss of oxygen content
of the atmosphere. It is shown that power and fuel consumption may be cor-
rected by subtracting observed water vapor pressure from atmospheric pressure
and using the result in place of barometric pressure in the usual correction
formula. The humidity correction may be as large as that due to changes in
barometric pressure.
Simple nomograms are presented for obtaining the humidity correction, both
near sea level and at higher altitudes. An appendix gives methods of computation
of these nomograms.

CONTENTS
Page
Introduction
I. 795
II. Test apparatus and procedure 795
1. Test series No. 1 797
2. Test series No. 2 797
3. Test series No. 3 798
III. Discussion of results 799
IV. Humidity correction chart 801
V. Conclusions 803
—
VI. Appendix Method of computation of charts 803

I. INTRODUCTION
Tests made by A. W. Gardiner x using a 1-cylinder engine having
indicated that atmospheric humidity has a very appreciable effect on
some phases of engine performance, a test program was undertaken
at the Bureau of Standards further to study this effect, using a
multi cylinder engine.

II. TEST APPARATUS AND PROCEDURE

Tests were made on a 6-cylinder, 3-port, overhead valve engine
of 3%-inch bore and 4%-inch stroke, coupled to a Sprague electric
dynamometer and spark accelerometer. In the three series of tests
three different fuels were used, being selected so as to give little or
no detonation at optimum spark advance under any test condition.
Power measurements were made on the dynamometer and friction
measurements by use of the spark accelerometer, 2 the latter being
iSee J. S. A. E., p. 155; February, 1929.
2 Method described in paper by Brooks on Operating Factors and Engine Acceleration presented at
S. A. E. annual meeting, January, 1929. See J. Soc. Automotive Eng., p. 130; August, 1929.

795
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796 Bureau of Standards Journal of Research [Vol. s

checked against friction measurements on the dynamometer. Humid-

ificationwas obtained by passing steam and cold air into a mixing
chamber and thence to an air heater. Measurements of humidity
were made by continuously passing a part of the carburetor air supply
over calibrated dry and wet bulb thermometers graduated to 0.2° F.
Measurements of humidity are expressed as pressure of water vapor
in mm Hg.

Figure 1. Effect of humidity on engine performance

Tests were made at full throttle at an engine speed of 500 r. p. m.

Cylinder and manifold jackets were maintained at the same tem-
perature, this being from 60° to 80° C. in the different series of tests
but being constant for any one series.
In the first two series of tests readings were taken at from 6 to 8
spark advances for each humidity and air-fuel ratio. From the
results, plotted against spark advance, faired values of maximum
power and optimum spark advance were obtained. In the third
test series optimum advance was found by trial.
 —
Brooks] Correcting Engine Tests for Humidity 797

1. TEST SERIES NO. 1

The tests of this series were made with a mixture of 2 parts of

eastern domestic aviation gasoline to 1 part of motor benzol. A
fixed carburetor adjustment was used, giving an air-fuel ratio of
about 13.5. Carburetor air temperature was maintained at 30° C.
Optimum power and spark advance were determined at humidities
from 5.1 mm Hg to saturation (31.9 mm
Hg). Figure 1 shows the
results, plotted against water vapor pressure.

Figure 2. Effect of humidity on power

2. TEST SERIES NO. 2

The tests of this series were made with a mixture of equal parts of
eastern domestic aviation gasoline and motor benzol. series of A
5 carburetor metering jets were used, giving air-fuel ratios from about
12 to about 16. Carburetor air temperature was maintained at
30° C.
With each air-fuel ratio optimum power and spark advance were
determined at two humidities, 4.5 and 27 Hg, respectively.mm
Figure 2 shows the results, plotted against water-vapor pressure.
It is notable that with orifice 43 an apparent increase of power with
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798 Bureau of Standards Journal of Research [Vols

humidity is shown. This is the leanest orifice used; the apparent

increase in power seems to be due to automatic enrichment of the
mixture at higher humidities.

3. TEST SERIES NO. 3

The tests of this series were made with a commercial brand of

aviation gasoline approximately equal in antiknock value to a mixture
of equal parts of eastern domestic aviation gasoline and motor benzol.

Figure 3. Effect of humidity on power

For this series of tests the carburetorwas equipped with a needle

valve, and were made over a range corresponding roughly to
tests
air-fuel ratios of 9 to 17. Carburetor air temperature was main-
tained at 41° C.
At two humidities, corresponding to 13.4 and 58.2 Hg, fuel mm
consumption, power, and optimum spark advance readings were
taken at 12 points over the range of air-fuel ratios stated above.
Results are shown in Figures 3 and 4.
 — 1

Brooks] Correcting Engine Tests for Humidity 799

III. DISCUSSION OF RESULTS

tests shown in Figure 1 indicate a linear relation between loss
The
ofpower and absolute humidity; the more extensive tests by Gardiner
agree with this. Moreover, if the humidity be expressed as per-
centage of barometric pressure, the loss of power in percentage is
roughly equal to the humidity. From this has arisen the "oxygen
content" hypothesis, stating that the power is proportional to the
oxygen content of unit volume of the atmosphere.

gfftt£
-j"t!Hfl# ill
1

1
1
mum ItttttifHi |ggfggfgg3ffl 1 illilltHITTI
'j:rn:g

1
.. ._

±F. :H:§

iffljjjjiji| t itfirr.l.ll

-Jf- f^

^^ilx^rr rrwri jfejiffi^S

Figure 4. Effect of humidity on specific fuel consumption

To test this hypothesis, values of loss of maximum power from the

three series of tests were plotted against the loss predicted on the basis
of the oxygen content hypothesis. Figure 5 shows the agreement be-
tween the measurements and the hypothesis, the weighted mean ob-
served loss of power being 101 per cent of that predicted. However,
other factors than decrease in oxygen content may affect the power.
Figure 6 summarizes the results in regard to variation of optimum
spark advance with humidity. A decided increase in spark advance
is seen to be required with increasing humidity. This rate of increase
seems to be a constant, irrespective of the magnitude of advance.
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800 Bureau of Standards Journal of Research [Vol. S

The upper curve is the mean by Gardiner on another

of observations
engine, operating at different speed and compression ratio and with
generally different operating conditions. For all these curves, how-
ever, the required advance is 2.1° per cm Hg of water-vapor pressure
within the limits of experimental error. On the basis of curves pre-
sented in N. A. C. A. Technical Eeport No. 276, and if the progress
of combustion is similar at all humidities, this rate of increase of spark
advance should entail a loss of power equal to 13 per cent of that due
to the decrease of oxygen; that only oxygen content and spark
is, if

advance affect the power, the loss of power should be 113 per cent of
that predicted on the basis of the "oxygen content " hypothesis.

Figure 5. Summary of tests showing effect of humidity on power

On the basis of the Bureau of Standards tests, which show but 101
per cent ±2.6 per cent of the loss predicted from the oxygen content
hypothesis, there is a 99.8 per cent probability that other factors tend
to compensate for the loss occasioned by reduction of oxygen and in-
crease of optimum spark advance. Such other factors may include
lower radiation, dissociation, and less change of specific heats, due to
lower maximum temperatures.
In Figure 4 it is seen that the specific fuel consumption curves at
the two humidities are displaced horizontally but have practically the
 —

Brooks] Correcting Engine Tests for Humidity 801

same minimum. Moreover, this horizontal displacement is equal, in

per cent, to the percentage difference in oxygen content. This in-
dicates that fuel consumption power should be corrected
as well as
for change in humidity, since fuel consumption is used in place of air-
fuel ratio. This has been done for test series No. 3, in Figure 7.
The results obtained at the two humidity values are seen to He on the
same curve within experimental error.

Figure 6. Effect of humidity on optimum spark advance

IV. HUMIDITY CORRECTION CHART

Figure 8 is a nomogram for obtaining water-vapor pressure (humid-
ity correction to barometer) from wet and dry bulb and barometer
readings. Figure 8 is constructed for units of °C. and Hg. Fig- mm
ure 9 is a similar nomogram for units of °F. and inches Hg.
To use these charts, place a straightedge so that it intersects the
t—f scale at the value of the difference between wet and dry bulb read-
ings and intersects the
t' scale at the value of the wet-bulb temperature.

At itspoint of intersection of the true (corrected) barometer value

read the humidity in the units shown on the scale at the extreme right.
For convenience a barometer-temperature correction nomogram
is located at the lower right of the chart. To use this, align a straight-
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802 Bureau of Standards Journal of Research [Vol. 8

edge through the center of the small circle at the bottom of the chart
and through the barometer temperature on the vertical scale to the
right. At its intersection with the observed barometer reading read
barometer correction on the same scale used for humidity correction.
This correction chart is for barometers with brass scales.

Figure 7. Verification of humidity correction to power and

fuel consumption

3
The humiditycharts are based on Smithsonian values for water-
vapor pressure and on the formula deduced by Professor Ferrel 4

- 0.00036750- o(l
>/
+Y5^)
for English units inwhich
6 = pressure
water vapor in inches Hg corresponding to dry
of
and wet bulb temperatures / and t' in °F., respectively.
B = true barometric pressure in Hg.
e' = saturation water-vapor pressure at f,

and on the same formula with appropriate constants for metric units.

8 Smithsonian Meteorological Tables.

i Annual Report of the Chief Signal Officer, Appendix 24, pp. 233-259; 1886.
 —

t = DRY BULB
t' = WET BULB
UNITS —°C 4 MM HG.

°1
-lOX -2
70Q 810
760

Figure 8. Nomogram for obtaining for humidity and barometer temperature

 t = DRY BULB
t'= WET BULB
UNITS -"FA IN. HG.

-I20
U100 f
h 80-
§60-
00 40-

Figtfre 9. Nomogram for obtaining for humidity and barometer temperature

 .

Brooks] Correcting Engine Tests for Humidity 803

It is to be noted that these charts assemble barometer corrections

significant in automotive work on one sheet, are sufficiently precise
for their purpose, and are less laborious and less productive of errors
of computation than psy chrome trie tables or contour charts. Other
barometer corrections include free-air altitude, latitude, and capil-
larity. The first two of these total less than 1 mm, while the latter
is of the opposite sign and of much the same magnitude; hence, these

three corrections are negligible for automotive work in this country.

In correcting engine-performance data to standard conditions cor-
rections for both humidity and barometer temperature are to be
subtracted from the observed barometer reading to give air pressure.
Observed power and corresponding fuel flow are then multiplied by
the pressure correction factor (standard pressure/air pressure), thus
allowing for variations in atmospheric pressure and humidity.

V. CONCLUSIONS
1. This work shows definitely that failure to allow for the effect of
differences in atmospheric humidity may introduce errors as great as
would be occasioned by failure to allow for changes in barometric
pressure. Under extreme conditions either correction may amount
to nearly 10 per cent of the indicated power.
2. Under all atmospheric conditions normally encountered in
automotive testing, humidity may be allowed for by deducting the
observed pressure of water vapor from the barometric pressure used
in the power computations.
3. Due to cancellation of opposing factors the proposed correction
represents the observed effect of humidity well within the usual pre-
cision of power measurements.
4. In correcting engine-performance data at different air-fuel ratios
the fuel flow values must be multiplied by the same coefficient as the
power values.
5. Optimum spark advance increases linearly with increasing
humidity.
6. Charts are presented for the convenient determination of
humidity values.

VI. APPENDIX— METHOD OF COMPUTATION OF CHARTS

The Ferrel formula for computation of absolute humidity viz,

€ = ^-0.000367^1 +yZ^y)(*-0 (1)

reduces, for a selected value of B, to

e = e'-{a + W) (t-f) (2)

where a and o are constants derived from the Ferrel formula, e' is

the water vapor pressure at f and e the absolute humidity at t, V

,
804 Bureau of Standards Journal of Research [Vol. 3

With this as a basis, the chart is constructed as follows: Suitable

scales are selected for (t — f) and for (e), as in Figure 10. Let the
length corresponding to one unit of (t—f) be m; the vertical length
corresponding to one unit of (e) be n; and the horizontal distance
between the '(t — f) and (e) scales be p. The f scale is then located

by the following considerations: When (t-f) is 0, the vapor pres-

sure obviously e', the saturation pressure at f.
is When (t — f) has

any value, the vapor pressure is

e1 = e -(a + bt
1
/
1
f
) ft-V) (2a)
Brooks] Correcting Engine Tests jor Humidity 805

If a linebe drawn from on the (t — tf) scale to e' on the (e) scale,
and another line from any other value on the (t—tf) scale to the cor-
responding value on the (e) scale as given by (2a), the intersection of
these lines fixes the corresponding value of t ' on the (tf) scale. In x

terms of the scale divisions, the equations of these lines are

v— —
nei
(3)

and

The solution for the point of intersection gives

pm
x= m + na + nbtf
(5)
_ mne
y m + na + nbtf
where subscripts have been dropped, as the solution is general, giving
the locus of the tf scale in terms of functions of tf. It is to be noted
that the solution for x and y does not contain ft — //); hence, the
requirements of equation (2) are satisfied by a lme. This verifies the
choice of the nomogram. From specific values of x and y from (5)
the tf scale is constructed.
In subsequently constructing scales for values at different baro-
metric pressures the following considerations apply. Since x and y
are now to be regarded as fixed, it is desired to alter p so that equation
(1) shall be satisfied at some other barometric pressure. "Calling the
new barometric pressure 7tB, and letting

Pi = value of p with B barometric pressure,

p 2 = value of p with JiB barometric pressure,

then, from (3),

(6)
Pi V2
where

n x
= value of n with B barometric pressure,

n^. = value of n with TiB barometric pressure.

Since x also is to be fixed, from (5)

Pim pm 2
(7)
m + ni(a+btf) m + njiia+btf)
 ALTITUDE, FT.

t - DRY BULB
t'
= WET BULB
UNITS-C 8, MM. HG.

Figure 11. Novwgram for determiniri; JnntiiiUlii at l,i(/l< nllilaihs

806 Bureau of Standards Journal of Research ivoi. $

Hence,

mpi + n2 hap t + njibt'pi — mp2 ~ n ap 2 — n x 1 bt'p 2 —

^ (Pi—p2)
=
=n ap2 (l — h) + n
1 1 bt
/
p2 (1 — h)
m = n p2 (a+W)
(j?i—p2 ) 1 (l — h)
p —p2 := n (a+bt')(l — h)
1 1

p2 m
Pi_~~
n (a+U
1
r
) (l — h) + m
p2 m
_ mpi
^2 ~m + 7i (l-W(a + M
1
/
)
ws
, ,

which defines p 2 and hence n2 in terms

, of known quantities.
Figure 11 is a chart for determining humidity in connection with
high altitude tests, constructed on the basis of (8). From this chart
it is seen that p 2 is sensibly constant with t'. Figures 8 and 9 are
based on the Smithsonian Tables, in which p 2 can be found from the
relation
p2 =p l -Tc (1-h) (9)

in which ~k is a constant for values of h near unity.

Washington, April 20, 1929.