The Theory and Practice of Model Aeroplaning Part 16

-- 7. TABLE OF SKIN FRICTION.

Per sq. ft. for various speeds and surface lengths.

-----------------+-------------+-------------+-------------+------------ Velocity of Wind | 1 ft. Plane | 2 ft. Plane | 4 ft. Plane | 8 ft. Plane -----------------+-------------+-------------+-------------+------------ 10 | 00112 | 00105 | 00101 | 000967 15 | 00237 | 00226 | 00215 | 00205 20 | 00402 | 00384 | 00365 | 00349 25 | 00606 | 00579 | 00551 | 00527 30 | 00850 | 00810 | 00772 | 00736 35 | 01130 | 0108 | 0103 | 0098 -----------------+-------------+-------------+-------------+------------

This table is based on Dr. Zahm's experiments and the equation

_f_ = 000000778_l_^{-007}_v_^{185}

Where _f_ = skin friction per sq. ft.; _l_ = length of surface; _v_ = velocity in feet per second.

In a biplane model the head resistance is probably from twelve to fourteen times the skin friction; in a racing monoplane from six to eight times.

-- 8. TABLE I.--(METALS).

--------------+------------+-----------------+------------- Material | Specific | Elasticity E[A] | Tenacity | Gravity | | per sq. in.

--------------+------------+-----------------+------------- Magnesium | 174 | | {22,000- | | | {32,000 Magnalium[B] | 24-257 | 102 | Aluminium- } | | | Copper[C]} | 282 | | 54,773 Aluminium | 26 | 111 | 26,535 Iron | 77 (about)| 29 | 54,000 Steel | 78 (about)| 32 | 100,000 Bra.s.s | 78-84 | 15 | 17,500 Copper | 88 | 36 | 33,000 Mild Steel | 78 | 30 | 60,000 | | | --------------+------------+-----------------+------------- [A] E in millions of lb. per sq. in.

[B] Magnalium is an alloy of magnesium and aluminium.

[C] Aluminium 94 per cent., copper 6 per cent. (the best percentage), a 6 per cent. alloy thereby doubles the tenacity of pure aluminium with but 5 per cent.

increase of density.

-- 9. TABLE II.--WIND PRESSURES.

_p_ = _kv_.

_k_ coefficient (mean value taken) 003 (miles per hour) = 00016 ft.

per second. _p_ = pressure in lb. per sq. ft. _v_ = velocity of wind.

Miles per hr. Ft. per sec. Lb. per sq. ft.

10 147 0300 12 176 0432 14 205 0588 16 235 0768 18 264 0972 20 2935 1200 25 367 1875 30 439 2700 35 513 3675

-- 10. Representing normal pressure on a plane surface by 1; pressure on a rod (round section) is 06; on a symmetrical elliptic cross section (axes 2:1) is 02 (approx.). Similar shape, but axes 6:1, and edges sharpened (_see_ ch. ii., -- 5), is only 005, or 1/20, and for the body of minimum resistance (_see_ ch. ii., -- 4) about 1/24.

-- 11. TABLE III.--LIFT AND DRIFT.

On a well shaped aerocurve or correctly designed cambered surface.

Aspect ratio 45.

Inclination. Ratio Lift to Drift.

0 19:1 287 15:1 358 16:1 409 14:1 478 12:1 573 96:1 718 79:1

Wind velocity 40 miles per hour. (The above deduced from some experiments of Sir Hiram Maxim.)

At a velocity of 30 miles an hour a good aerocurve should lift 21 oz.

to 24 oz. per sq. ft.

-- 12. TABLE IV.--LIFT AND DRIFT.

On a plane aerofoil.

N = P(2 sin {alpha}/1 + sin {alpha})

Inclination. Ratio Lift to Drift.

1 583:1 2 292:1 3 193:1 4 143:1 5 114:1 6 95:1 7 80:1 8 70:1 9 63:1 10 57:1

P = 2_kd_ AV sin {alpha}.

A useful formula for a single plane surface. P = pressure supporting the plane in pounds per square foot, _k_ a constant = 0003 in miles per hour, _d_ = the density of the air.

A = the area of the plane, V relative velocity of translation through the air, and {alpha} the angle of flight.

Transposing we have

AV = P/(2_kd_ sin {alpha})

If P and {alpha} are constants; then AV = a constant or area is inversely as velocity squared. Increase of velocity meaning diminished supporting surface (_and so far as supporting surface goes_), diminished resistance and skin friction. It must be remembered, however, that while the work of sustentation diminishes with the speed, the work of penetration varies as the cube of the speed.

-- 13. TABLE V.--TIMBER.

Column Headings:

A. Material B. Specific Gravity C. Weight per Cub. Ft. in Lb.

D. Strength per Sq. In. in Lb.

E. Ultimate Breaking Load (Lb.) span 1' x 1" x 1"

F. Relative Resilience in Bending G. Modulus of Elasticity in millions of Lb. per Sq. In. for Bending H. Relative Value. Bending Strength compared with Weight

---------------+-----+-------+-------------+-------+-----+-----+---- A |B | C | D |E |F |G | H ---------------+-----+-------+-------------+-------+-----+-----+---- Ash | 79 | 43-52 |14,000-17,000| 622 |469 |155 |130 Bamboo | | 25[A]| 6300[53] | |307 |320 | Beech | 69 | 43 |10,000-12,000| 850 | |165 |198 Birch | 71 | 45 | 15,000 | 550 | |328 |122 Box |128 | 80 |20,000-23,000| 815 | | |102 Cork | 24 | 15 | | | | | Fir (Norway | | | | | | | Spruce) | 51 | 32 | 9,000-11,000| 450 |301 |170 |140 American | | | | | | | Hickory | | 49 | 11,000 | 800 |347 |240 |163 Honduras | | | | | | | Mahogany | 56 | 35 | 20,000 | 750 |340 |160 |214 Maple | 68 | 44 | 10,600 | 750 | | |170 American White | | | | | | | Pine | 42 | 25 | 11,800 | 450 |237 |139 |180 Lombardy Poplar| | 24 | 7,000 | 550 |289 | 077|229 American Yellow| | | | | | | Poplar | | 44 | 10,000 | |363 |140 | Satinwood | 96 | 60 | |1,033 | | |172 Spruce | 50 | 31 | 12,400 | 450 | | |145 Tubular Ash, | | | | | | | _t_ = 1/8 _d_ | | 47 | | |350 |155 | ---------------+-----+-------+-------------+-------+-----+-----+----

_t_ = thickness: _d_ = diameter.

[A] Given elsewhere as 55 and 22,500 (_t_ = 1/3_d_), evidently regarded as solid.

-- 14.--=Formula connecting the Weight Lifted in Pounds per Square Foot and the Velocity.=--The empirical formula

W = (VC)/_g_

Where W = weight lifted in lb. per sq. ft.

V = velocity in ft. per sec.

C = a constant = 0025.

_g_ = 322, or 32 approx.

may be used for a thoroughly efficient model. This gives (approximately)

1 lb. per sq. ft. lift at 25 miles an hour.

21 oz. " " 30 "

6 oz. " " 15 "