gliding angle 1 in 7,

and the average width

of the struts about 1

inch (the exact breadth

assumed depending on

the form and strength

of the section).

Then, since gliding

W

angle = ^- , every /

pounds of strut

\vright will give rise to 1 pound of resistance, in addition to

the aerodynamic resistance of the struts.f We can, therefore,

W

write T = 1- R, where T = thrust due to the struts, and

It is their aerodynamic resistance. Simplifying, we have

G = W + 7R, but, since this expression has a maximum value

for the least efficient strut, the reciprocal is here employed,

14300

and multiplied by the constant 14300, giving C = = jp i 7^

The best strut under the conditions above specified is then

the one showing the highest value for C. The reason for

choosing this particular value for the multiplier is that it

makes C = 100 for the best strut of the first and largest series

which we shall consider.

If the speed of the machine for which the struts are being

selected is greater than 60 miles an hour, the resistance be-

comes of greater importance as compared with the weight,

and the merit factors for those sections which, although heavy,

offer very low resistances are relatively improved. If the glid-

ing angle is flatter than 1 in 7, a similar effect ensues.

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On the other hand, if it becomes necessary to use struts

having a diameter of more than 1 inch or thereabouts, the ad-

OGILVIE'S SECTIONS

vantage inclines toward the sections which have the greatest

strength for their weight, and the relative importance of re-

sistance is diminished, since, in similar sections, weight varies

as the square of the breadth and resistance only as the first

power. These effects are, however, of slight importance, and

would not be likely to change the merit factors enough to have

serious influence on the choice of a section in any given case.

The question of strength will be taken up more fully in

another section of the course. It will suffice to say here that

the strengths of two struts have been considered to be equal

when their moments of inertia about their longitudinal axes

are equal.

Strut Sections Developed by Ogilvie

We may now proceed to the examination of definite data for

a number of series of struts, tested at various times and places.

The following figures are the result of experiments performed

at the N. P. L. at the suggestion of Alec Ogilvie, the sections

being illustrated in Fig. 1.

/ = moment of inertia for the section in question about its

longitudinal axis (inches* for a strut 1 inch wide).

R = resistance in pounds of 100 feet of strut 1 inch wide at

60 miles per hour.

W = weight in pounds of 100 feet of spruce strut 1 inch

wide.

b = width of strut whose strength will be equal to that of a

strut of section a, and 1 inch wide.

W = weight of 100 feet of spruce strut of width b.

C M = merit factor at 60 miles per hour.

No.

W

W

a

.167

104.4

41.6

1.00

41.8

19

b

.049

81.9

16.4

1.36

30.3

18

c

.090

59.2

30.4

1.17

41.6

27

d

.124

36.9

34.8

1.08

40.6

45

e

.074

63.0

33.4

1.23

50.6

24

1

.134

28.6

37.7

1.06

42.4

56

.094

54.9

30.0

1.15

39.7

30

h

.119

12.8

39.7

1.09

47.1

99

i

427

12.8

41.0

1.07

47.0

100

;

.119

13.5

39.7

1.09

47.1

96

i

.111

13.5

38.0

1.11

46.8

94

I

.106

29.9

36.4

1.12

45.6

51

m

.106

45.9

36.6

1.12

45.9

35

n

.171

14.2

51.9

0.99

509

97

o

.146

13.5

47.0

1.03

49.9

97

p

.128

18.7

44.1

1.07

50.5

75

q

.245

15.1

71.0

0.91

58.9

93

r

.227

16.4

67.2

0.93

58.1

87

s

.194

13.5

62.0

0.96

57.2

97

t

.209

13.5

66.1

0.95

59.7

95

.115

24.6

42.5

1.10

51.4

59

t Relationships between weight and resistance on a glide will be

fully considered in Section 12.

Many very interesting conclusions can be drawn from this

table. In the first place, it is evidently of the utmost im-

portance to avoid rapid changes in curvature. Several sec-

tions, notably, e and I, although they appear to have a very

smooth outline, oppose a large resistance simply because the

transition from the entrance to the run is so abrupt that the

air-flow cannot follow its contour, and violent eddy-making

ensues.

8fi

AERODYNAMICAL THEORY AND DATA

The good performance of several sections so formed indi-

cates that it may be wise actually to run the sides of the strut

parallel for some little distance, as illustrated by q and t.

This is counteracted, however, by the fact that skin-friction

increases in proportion to the " wetted surface " of the strut.

It is for this reason that the very longest sections did not give

such low resistances as those of more moderate form. This

matter of the ratio of length of section to width will be dis-

cussed more fully somewhat later, in connection with another

series of tests.

It will be seen, too, that the resistance is little affected by

the chopping off of a portion of the tail in such a manner as

to leave it straight across. Examples of this are furnished

by n, ( and i. This is due to the fact that it has not been pos-

sible in any strut yet designed to totally eliminate the region

of deadwater behind the strut. As will be evident from any

section of air-flow about a fair-shaped section, the lines of

flow always leave the contour of the strut some distance short

of the extreme rear. Since no changes made in the contour

within this region will have any decided effect on the re-

sistance, it avails nothing to go to the trouble and expense

involved in the attempt to construct a wooden strut running

out to a sharp point at the back.

Another Series of Struts Tested at the N. P. L.

At about this same time another series of struts was tested

at the same laboratory, the sections being those actually em-

Dt Haulllant

Beta

B.F.34

c

Baby

FIG. 2. STRUT SECTIONS

TESTED AT N. P. L.

G>

PIG. 3. N. P. L.

STRUTS

ployed in machines then existing. The outlines of the sections

tested are shown in Fig. 2, and the characteristics are given

below.

Blerlot A 070

Bleriot B 107

Fmrma n 074

De Harilland. .052

Baby 110

B.F. 34 279

B.F. 35 238

188

K

51.0

52.7

49.3

54.9

17.0

i: -..r.

13.5

14.8

34.9

25.2

20.5

41.6

93.2

si! 7

61.7

b

1.24

1.11:

1.22

1 .:;

1.11

-v

0.92

0.97

40.0

43.8

36.8

r,i.:.

n.9

70.0

58.0

Om

80

31

26

7K

90

of the symbols being the same as in the tables already given,

except that n = the ratio of the length to width of section.

n

2.

2.5

3.

3.5

4.

4.5

5.

.094

.117

.141

.104

.iss

.211

.235

R

24.8

13.7

13.4

11.4

11.2

11.7

12.1

W

32.0

40.0

48.1

50.1

04.1

72.1

80.1

b

1.15

1.0!)

1.04

1.00

0.97

O.94

0.92

W

42.3

47.5

52.1

M.1

)i'J.'J

67.8

73.7

59

94

9(i

in:,

LOS

99

94

Tims it is apparent that the best of these sections are inatc-

rinlly superior to the best of the sections tested by Ogilvie.

both in resistance and in merit factor. In Fig. 4 resistance of

RESISTANCE

OP

R.A.K STRUTS

FIG. 4.

UESISTAVCE AND FACTORS OP MEKIT FOR R. A.

STRUTS

100 feet of strut at 60 miles per hour, and merit factor at 60

miles per hour, are plotted against ratio of length to width.

As this ratio diminishes, the air-flow about the strut takes on

a very uncertain character, and the values when n is less than

2 are rather doubtful. Such extremely short sections as this

are also undesirable from the standpoint of lateral stability.

as will be shown in another section of the Course. On the

other hand, n may be considerably pi-eater than the absolute

optimum value without any great disadvantage, so it will be

well in general to employ a ratio of four, or even a slightly

higher figure. The photographs of Mow aliout strut sections.

reproduced in Fig. ~>. show clearly why such a procedure c-.-m

be safely adopted.

It will be seen that these figures simply supplement and

confirm the conclusions already deduced from the more exten-

sive and systematic investigations directed by Mr. Ogilvie.

TeU on Struts, Length to Width Varied

As a result of these and other tests. series of struts em-

bodying the best features of those already tried, and varying

only in the ratio of length of section to width, was made and

tested at the National Physical laboratory. Three rep re

live members of tin- series are shown in Fig. .'!. The table

below gives the characteristics of these struts, the meaning

Two Kiffcl Struts

Two struts of somewhat the same section as those just di-

eiisscd have recently l.een I, '-led by Kifl'el. and show remark-

ably low resistances. Their outlines arc uivcn in Fiir. (i. For

Xo. 1, having n equal to :!.L'.'I, If equals !i.7 pounds, while for

No. 2. with a somewhat sharper entry, i is L'.lKi and R is only

8.7 pounds. I'arl of this improvement oxer the best of the

Knglish tests, hoxvexei. i- undoubtedly due to the higher wind

speed which is secured in Kiffel's laboratory, the resistance

coefficient having a tendency to rise as the speed of test i^.

decreased.

AERODYNAMICAL THEORY AND DATA

67

Effect of Length of Struts

We now turn our attention to the effect of the length of

the strut. While this point is less important than was gen-

erally supposed a few years ago, and while its effects are

largely determined by the nature of the surfaces in which the

strut terminates, the experimental results bearing on the mat-

ter should nevertheless be studied. For this data we are

indebted to Mr. Thurston, who has described his results in

the series of articles already cited. As the result of a great

nel would be exceedingly difficult to devise. The matter might

well be investigated in an outdoor, full-scale plant such as

that at St. Cyr.

Resistance of Inclined Struts

The only point which remains to be studied is the resistance

of struts which are not normal to the line of flight. Some

much more recent tests by Mr. Thurston have covered this

point, and show very surprising results. Struts of square,

rectangular, circular, and stream-line section were tested at

angles from to 90 degrees, and the effects of the ends of the

strut offering a direct resistance when inclined were overcome

by the use of the method of differences: that is, tests were

made first on a strut 34 inches long, and then on one 16

inches long, the difference of the figures obtained being equal

to the resistance of an 18-inch section of an infinite strut.

The ratio of the resistance of a strut inclined at various

BETA

FIG. 5.

DE HAVILLAND

ILLUSTRATING FLOW AROUND STRUTS

many experiments on manifold different types of strut, he

came to the conclusion that resistance for a strut with free

ends could best be expressed by the formula B = KltV 1 -

.0073fF 2 , where R is the resistance in pounds, I and *, re-

spectively, the length and thickness of the strut in feet, K a

constant, and V the speed in miles per hour.

It is evident from this equation that, even with the lowest

values of K yet obtained, the effects of length will be prac-

Fio. 6. Two EIFFEL STRUTS

tically negligible when the length is more than 50 times the

thickness, as it generally is. Since, in addition, the case of a

strut with free ends is one which never occurs in practise,

resistance may be considered as independent of length-thick-

ness ratio for all the purposes of design.

The form of air-flow about the wing may have very decided

effects on the resistance of interplane struts, but we have no

means of knowing how great these aro. and experiments cover-

ing this point and susceptible of performance in a wind tun-

INCMMATIOM Of BAH TO WIMO

FIG. 7. DATA FOR INCLINED STRUTS

angles to the resistance of a normal strut of like section and

equal projected length is plotted in Fig. 7. It will be seen

that the resistance at 30 degrees to the wind is less than one-

third of that at 90 degrees, and this large difference is by no

means accounted for by the difference in length of section

parallel to the wind. When a circular strut is placed at an

angle of 30 degrees to the wind, the section parallel thereto

is an ellipse having a length of twice its width, and the resist-

ance of an elliptical strut such as this, when placed normal.

is only 36 per cent less than that for a circular section.

About 45 per cent of the reduction due to inclination thus

remains unaccounted for.

Since, however, the curve of reduction is substantially a

sine curve, and is therefore very flat at the ends, there is

very little advantage to be gained from inclining a stream-

line strut unless it is inclined at least 30 degrees to the nor-

mal. This reduced resistance should, however, be kept in

mind as a point in favor of the staggered biplane. Eiffel

also made a few tests on struts inclined 30 degrees from the

normal, the results cheeking very well with Mr. Thurston's.

The Effect of Changing the DV Product for Struts

As was shown in Chapter 10, the resistance coefficient is

not an absolute constant, but is a function of VI), when-

V Is the speed and I) the diameter of the strut. The coeffi-

cient tends to decrease as VI) increases, but the change for

values of I'D (in foot/second units) above 6 is extremely small,

as Eiffel lias demonstrated. The tests made at thp National

Physical Laboratory have been made with a value of VD

equal to only 2.5. whereas, in an actual machine, this quantity

would never be likely to fall below 5, and is generally from

7 to 10.

i is AERODYNAMICAL THEORY AND DATA

We can therefore deduce from Kitlel's experiments that it References for Part I. Chapter 11

is safe to reduce the values for resistance here given (for the

N. P. L. tests) by about 25 per cent in applying them to a " strut*." FHoht. June is. 1012.

design. This indicates that, as was hinted above, the superior- -Aerodynamic RMMUM of struts. Bare, and wires." by A. v.

ity of Eiffel's strut sections is more apparent than real, and Thurston ; Aeronautical Journal, April and July, 191::.

that the best sections yet available are the N. P. L. sections Technical Reports of the British Advisory Committee on Aeronautics.

having fineness ratios of from 3.5 to 4.5. The correction 1911-12. 1912-13.

given here should be applied only to Struts of fairly good "The Resistance of Inclined Struts In a Uniform Air Curri'iit," by A.

section, as the value of VD has much less effect on those sec- i^ 1 " 1 "" " " Dd "' Tonnsteln ' Aeron <"" lcal """' Janu "5'-

tions for which the resistance is relativelv IUL-II. and in which

" Nouvelles Recbercues sur In Resistance de 1'Alr et 1'Avlatlon." by G.

there is more effect due to turbulence than to skin friction. Eiffel. (1914 edition.)

Chapter XII

Resistance and Performance

Nomenclature

It may be useful to restate the symbols which we employ

in considering performance curves, ascent and descent.

IT" = weight of the machine;

A = area of the wings.

i = angle of incidence of the wings.

L = lift.

K u = lift coefficient.

D = drag of wings.

K., = drag coefficient.

11 = resultant of lift and drag on the wings.

P = parasite or structural resistance of a machine.

Dt = total resistance or drag = T) -\- P.

R t = total resultant air force on a machine.

// = -propeller thrust.

6 = angle of flight path with the horizontal.

Structural and Wing Resistance for the British B.E.2

In Chapter 4, a problem was worked out on the sustentation

and resistance of wing surfaces, which in spite of some rough

50 00

MILES PER HOUR

FIG. 1. PERFORMANCE CURVES FOR THE B.E.2

assumptions, illustrated the main performance curves and cal-

culations employed. In Fig. 1 are shown curves for the Brit-

ish B. E. 2. It is not a particularly modern machine, but has

been worked out so thoroughly that it deserves particularly

careful study.

The body or parasite resistance which includes the resis-

tance of the wing bracing, chassis, etc.. as well as the resistance

of the body proper, is taken as varying as T'" 2 and allowance

has been made for propeller slip stream velocity. The body

resistance is seen to play an unimportant part at low speeds.

But at about 53 miles per hour it becomes greater than the

plane or wing resistance, and at high speeds it. is almost twice

as great as the wing resistance. This emphasizes the imppr-

tance of minimizing the resistance for a high-speed machine.

However good a wing section itself may be, high structural

resistance will make high speeds impossible.

The plane resistance curve has a minimum value at about

65 miles per hour and increases on either side of this speed.

It is interesting to follow out how this increase in resist-

ance on either side occurs. At high speeds, the angles of

incidence and the drift coefficients are small but the speeds

are very great, and the increase in wing resistance is obvious.

At small speeds on the other hand the airplane is flying at

large angles of incidence to give the necessary sustentation and

the drift coefficients are large. The shape of the total re-

sistance curve follows from the summation of the two.

Theoretical Laws for Minimum Thrust and

Minimum Horsepower

From a theoretical treatment of the question, the following

interesting law has been derived :

Minimum thrust is required to overcome the resistance of an

airplane when Hie parasite resistance is equal to the drag of

the wings.

For a proof of this law, reference to Chasseriaud and

Espitallier is appended. In the case we have selected, illus-

trated in Fig. 1, the structural air resistance and the wing

drag are equal at a speed of 53 miles an hour, while the

minimum resistance is at 49 miles per hour. The law does not

seem to be borne out by practice, though it may be occasion-

ally useful as a rough check.

The minimum horsepower required generally occurs at a

low speed, but not at the minimum speed; and its position

will vary for every machine. Another theoretically deduced

law states that:

Minimum horsepower is required irln'ii Hie machine is mov-

ing at a speed at which the wing resistance is three times the

body resistance.

" This law is often highly inaccurate, but may be useful.

Effective or Propeller Horsepower Available Curve

Typical curves for these are also illustrated in Fig. 1, and

are of the greatest interest to the designer. In establishing

such curves it is generally assumed that the engine is running

at the rated revolutions per minute and that in designing the

propeller the efficiency for this revolution per minute at every

airplane speed is known. Thus assuming an engine which

delivers 140 horsepower at an ail-plane speed of 80 miles an

hour, the propeller having an efficiency of 75 per cent at this

speed, the available horsepower will be

140 X 75

100

= 105 horsepower.

69

70

AERODYNAMICAL THEORY AND DATA

Since the power of a propeller is given by the product of

us thrust into the speed and the speed of the propeller is the

speed of the airplane, it follows that when the propeller is

delivering sufficient power, it is also delivering sufficient

thrust. Hence propeller horsepower available is sufficient for

all practical consideration, and propeller thrust curves need

not be included in a performance chart.

Minimum and Maximum Speed; Maximum Excess

Power; Best Climb; Descent

The maximum and minimum speeds of an airplane are gen-

erally given by the two points of intersection of the propeller

horsepower available and the total horsepower required. If

the machine is highly- powered, and the propeller efficient, the

two curves may not intersect at the speed at which the lift

becomes insufficient, and the airplane would climb at stalling

angle, unless the engine is considerably throttled down. The

climb decreases the angle of incidence, and checks stalling.

It is thus a decided advantage to have excess available power

at high angles.

It is a simple matter to deduce the speed of climb from the

excess power. This is absorbed in raising the machine.

Ex

power

Total weight X climb per second

551)

The maximum excess power does not occur at the lowest

speed. To find it, we must measure the maximum ordinate

between the available propeller horsepower and the total re-

quired horsepower. In Fig. 1 this is to be found at 48 miles

per hour. The excess is 21 horsepower and the weight of the

machine is 1650 pounds.

Climb =

21 X 550

= 7 feet per second or 420 feet per min-

ute. This is, however, only the initial rate of climb. As the

machine rises, the density of the air, the power of the engine,

and the climb gradually diminish.

In practice, the pilot need not know the change of in-

cidence that he produces to climb, although for a given ma-

chine it is an easy matter to calculate the correct angle from

the performance curves. In Dr. Hunsaker's words, " a care-

ful man moves his elevator slowly until he has placed him-

self on the desired trajectory." Part of the art of aviation is

to do this without exceeding safe limits, for obviously there is

a limit to the rate of climb the engine can handle. If the

machine is put on a climb too steep for the power of the ma-

chine, the speed is suddenly lost, the controls become ineffec-

tive, and the machine has stalled.

In descent, very analogous considerations obtain. The

pilot decreases his angle of incidence to a negative value. At

this angle the speed required for sustentation is beyond that

of the maximum, and the propeller horsepower is insufficient.

If D = deficiency in horsepower,

n Total weight X velocity of descent.

Mt

The machine descends and gains the required speed under tin-

action of gravity.

The Two Regions of Control. Control by I limiilin-

Consider the performance curves of the same machine, the

Hnti-h I'..K.'_' shown in Fig. 1. Suppose the machine to be

flown iit in degrees at the point J/ with the engine throttled.

so that there is equilibrium, and the power curve is as shown.

26 horsepower. The pilot wishing t<> rise will naturally in

crease his angle of incidence to say 12 degrees. He will thru

require 30 horsepower while the throttled engine will deliver

even less than the 2(j horsepower through the propeller. In-

stead of rising the machine will fall.

Suppose now that flying at the same point and under the

same conditions he wishes to descend, and decreases his angle

to 8 degrees. He will now have an excess of power of 3

horsepower as can be seen from the curves and will ascend

instead of descend. There is therefore a region of reverse

controls, known to French authors as the regime lent.

At the point M . when the pilot wishes to rise and in-

creases his angle of incidence, he does indeed obtain excess

power and rises. Here the controls are normal and the region

is known as regime rapide. For an inexperienced pilot the

regime lent is dangerous. Even if he knows the angle of in-

cidence at which he is working, he is likely to get into diffi-

culties.

With a flexible engine, an expert pilot can operate an air-

plane in the slow speed region by manipulation of the throttle

40 M 60 TO SO 90 100

MILES PEU HOUR

Fiu. 2. VARYING SPEED RANGE WITH ENGINE THROTTLED

alone. In Fig. 2 the propeller horsepower available is shown

with the engine throttled down to various speeds for a design

taken i'rom Dr. Hunsaker's pamphlet, to which reference is

appended. For each speed of the engine there is a different

maximum and minimum speed of the airplane, and a different

speed range. If the airplane is living at the minimum speed

in the regime lent region at a certain revolution per minute,

the pilot can by unthrottling his engine pass to a larger speed

!.-iii'_ r e, obtain excess power and climb without changing his

forward speed or angle of incidence. When an engine is

throttled the danger of reversed controls is still greater, lie-

cause the speed range becomes so very small. Kven the best

of pilots may mistake his position on the curve.

In French airplane contests, a premium has been placed on

low speeds, and the regime lent with throttling has been

largely and successfully used. Such operation does not seem

advisable for ordinary flying.

Variations in PropHIrr Horsepower (lunr-

We will now consider the possible variations in performance

by changing the design of the propeller from a high speed to