CHAPTER XIV.

USEFUL NOTES, TABLES, FORMULÆ, ETC.

§ 1. COMPARATIVE VELOCITIES.

Miles per hr. Feet per sec. Metres per sec. 10 = 14·7 = 4·470 15 = 22 = 6·705 20 = 29·4 = 8·940 25 = 36·7 = 11·176 30 = 44 = 13·411 35 = 51·3 = 15·646

§ 2. A metre = 39·37079 inches.

_In order to convert_:-- Metres into inches multiply by 39·37 " feet " 3·28 " yards " 1·09 " miles " 0·0006214 Miles per hour into ft. per min. multiply by 88·0 " min. " sec. " 88·0 " hr. into kilometres per hr. " 1·6093 " " metres per sec. " 0·44702 Pounds into grammes multiply by 453·593 " kilogrammes " 0·4536

§ 8. Total surface of a cylinder = circumference of base × height + 2 area of base.

Area of a circle = square of diameter × 0·7854.

Area of a circle = square of rad. × 3·14159.

Area of an ellipse = product of axes × 0·7854.

Circumference of a circle = diameter × 3·14159.

Solidity of a cylinder = height × area of base.

Area of a circular ring = sum of diameters × difference of diameters × 0·7854.

For the area of a sector of a circle the rule is:--As 360 : number of degrees in the angle of the sector :: area of the sector : area of circle.

To find the area of a segment less than a semicircle:--Find the area of the sector which has the same arc, and subtract the area of the triangle formed by the radii and the chord.

The areas of corresponding figures are as the squares of corresponding lengths.

§ 4. 1 mile = 1·609 kilometres. 1 kilometre = 1093 yards. 1 oz. = 28·35 grammes. 1 lb. = 453·59 " 1 lb. = 0·453 kilogrammes. 28 lb. = 12·7 " 112 lb. = 50·8 " 2240 lb. = 1016 " 1 kilogram = 2·2046 lb. 1 gram = 0·0022 lb. 1 sq. in. = 645 sq. millimetres. 1 sq. ft. = 0·0929 sq. metres. 1 sq. yard = 0·836 " 1 sq. metre = 10·764 sq. ft.

§ 5. One atmosphere = 14·7 lb. per sq. in. = 2116 lb. per sq. ft. = 760 millimetres of mercury.

A column of water 2·3 ft. high corresponds to a pressure of 1 lb. per sq. in.

1 H.P. = 33,000 ft.-lb. per min. = 746 watts.

Volts × amperes = watts.

{pi} = 3·1416. _g_ = 32·182 ft. per sec. at London.

§ 6. TABLE OF EQUIVALENT INCLINATIONS.

Rise. Angle in Degs. 1 in 30 1·91 1 " 25 2·29 1 " 20 2·87 1 " 18 3·18 1 " 16 3·58 1 " 14 4·09 1 " 12 4·78 1 " 10 5·73 1 " 9 6·38 1 " 8 7·18 1 " 7 8·22 1 " 6 9·6 1 " 5 11·53 1 " 4 14·48 1 " 3 19·45 1 " 2 30·00 1 " {square root}2 45·00

§ 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_ = 0·00000778_l_^{-0·07}_v_^{1·85}

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 | 1·74 | | {22,000- | | | {32,000 Magnalium[B] | 2·4-2·57 | 10·2 | Aluminium- } | | | Copper[C]} | 2·82 | | 54,773 Aluminium | 2·6 | 11·1 | 26,535 Iron | 7·7 (about)| 29 | 54,000 Steel | 7·8 (about)| 32 | 100,000 Brass | 7·8-8·4 | 15 | 17,500 Copper | 8·8 | 36 | 33,000 Mild Steel | 7·8 | 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_ = _kv²_.

_k_ coefficient (mean value taken) ·003 (miles per hour) = 0·0016 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 14·7 0·300 12 17·6 0·432 14 20·5 0·588 16 23·5 0·768 18 26·4 0·972 20 29·35 1·200 25 36·7 1·875 30 43·9 2·700 35 51·3 3·675

§ 10. Representing normal pressure on a plane surface by 1; pressure on a rod (round section) is 0·6; on a symmetrical elliptic cross section (axes 2:1) is 0·2 (approx.). Similar shape, but axes 6:1, and edges sharpened (_see_ ch. ii., § 5), is only 0·05, 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 4·5.

Inclination. Ratio Lift to Drift. 0° 19:1 2·87° 15:1 3·58° 16:1 4·09° 14:1 4·78° 12:1 5·73° 9·6:1 7·18° 7·9:1

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 + sin² {alpha})

Inclination. Ratio Lift to Drift. 1° 58·3:1 2° 29·2:1 3° 19·3:1 4° 14·3:1 5° 11·4:1 6° 9·5:1 7° 8·0:1 8° 7·0:1 9° 6·3:1 10° 5·7:1

P = 2_kd_ AV² sin {alpha}.

A useful formula for a single plane surface. P = pressure supporting the plane in pounds per square foot, _k_ a constant = 0·003 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

AV² = P/(2_kd_ sin {alpha})

If P and {alpha} are constants; then AV² = 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 |4·69 |1·55 |13·0 Bamboo | | 25[A]| 6300[53] | |3·07 |3·20 | Beech | ·69 | 43 |10,000-12,000| 850 | |1·65 |19·8 Birch | ·71 | 45 | 15,000 | 550 | |3·28 |12·2 Box |1·28 | 80 |20,000-23,000| 815 | | |10·2 Cork | ·24 | 15 | | | | | Fir (Norway | | | | | | | Spruce) | ·51 | 32 | 9,000-11,000| 450 |3·01 |1·70 |14·0 American | | | | | | | Hickory | | 49 | 11,000 | 800 |3·47 |2·40 |16·3 Honduras | | | | | | | Mahogany | ·56 | 35 | 20,000 | 750 |3·40 |1·60 |21·4 Maple | ·68 | 44 | 10,600 | 750 | | |17·0 American White | | | | | | | Pine | ·42 | 25 | 11,800 | 450 |2·37 |1·39 |18·0 Lombardy Poplar| | 24 | 7,000 | 550 |2·89 | 0·77|22·9 American Yellow| | | | | | | Poplar | | 44 | 10,000 | |3·63 |1·40 | Satinwood | ·96 | 60 | |1,033 | | |17·2 Spruce | ·50 | 31 | 12,400 | 450 | | |14·5 Tubular Ash, | | | | | | | _t_ = 1/8 _d_ | | 47 | | |3·50 |1·55 | ---------------+-----+-------+-------------+-------+-----+-----+----

_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 = (V²C)/_g_

Where W = weight lifted in lb. per sq. ft. V = velocity in ft. per sec. C = a constant = 0·025. _g_ = 32·2, 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 " 4 oz. " " 12 " 2·7 oz. " " 10 "

Remember the results work out in feet per second. To convert (approximately) into miles per hour multiply by 2/3.

§ 15. =Formula connecting Models of Similar Design, but Different Weights.=

D {proportional to} {square root}W.

or in models of _similar design_ the distances flown are proportional to the square roots of the weights. (Derived from data obtained from Clarke's flyers.)

For models from 1 oz. to 24-30 oz. the formula appears to hold very well. For heavier models it appears to give the heavier model rather too great a distance.

Since this was deduced a 1 oz. Clarke model of somewhat similar design but longer rubber motor has flown 750 ft. at least; it is true the design is not, strictly speaking, similar, but not too much reliance must be placed on the above. The record for a 1 oz. model to date is over 300 yards (with the wind, of course), say 750 ft. in calm air.

§ 16. =Power and Speed.=--The following formula, given by Mr. L. Blin Desbleds, between these is--

W/W{0} = (3_v{0}_)/(4_v_) + ¼(_v_/_v{0}_)³.

Where _v{0}_ = speed of minimum power W{0} = work done at speed _v{0}_. W = work done at speed _v_.

Making _v_ = 2_v{0}_, i.e. doubling the speed of minimum power, and substituting, we have finally

W = (2-3/8)W{0}

i.e. the speed of an aeroplane can be doubled by using a power 2-3/8 times as great as the original one. The "speed of minimum power" being the speed at which the aeroplane must travel for the minimum expenditure of power.

§ 17. The thrust of the propeller has evidently to balance the

Aerodynamic resistance = R The head resistance (including skin friction) = S

Now according to Renard's theorem, the power absorbed by R + S is a minimum when

S = R/3.

Having built a model, then, in which the total resistance

= (4/3)R.

This is the thrust which the propeller should be designed to give. Now supposing the propeller's efficiency to be 80 per cent., then P--the minimum propulsion power

= (4/3)R × 100/80 × 100/75 × _v_.

Where 25 per cent. is the slip of the screw, _v_ the velocity of the aeroplane.

§ 18. =To determine experimentally the Static Thrust of a Propeller.=--Useful for models intended to raise themselves from the ground under their own power, and for helicopters.

The easiest way to do this is as follows: Mount the propeller on the shaft of an electric motor, of sufficient power to give the propeller 1000 to 1500 revolutions per minute; a suitable accumulator or other source of electric energy will be required, a speedometer or speed counter, also a voltmeter and ammeter.

Place the motor in a pair of scales or on a suitable spring balance (the former is preferable), the axis of the motor vertical, with the propeller attached. Rotate the propeller so that the air current is driven _upwards_. When the correct speed (as indicated by the speed counter) has been attained, notice the difference in the readings if a spring balance be used, or, if a pair of scales, place weights in the scale pan until the downward thrust of the propeller is exactly balanced. This gives you the thrust in ounces or pounds.

Note carefully the voltage and amperage, supposing it is 8 volts and 10 amperes = 80 watts.

Remove the propeller and note the volts and amperes consumed to run the motor alone, i.e. to excite itself, and overcome friction and air resistance; suppose this to be 8 volts and 2 amperes = 16; the increased load when the propeller is on is therefore

80 - 16 = 64 watts.

All this increased power is not, however, expended on the propeller.

The lost power in the motor increases as C²R.

R = resistance of armature and C = current. If we deduct 10 per cent. for this then the propeller is actually driven by 56 watts.

Now 746 watts = 1 h.p.

{therefore} 56/746 = 1/13 h.p. approx.

at the observed number of revolutions per minute.

§ 19. N.B.--The h.p. required to drive a propeller varies as the cube of the revolutions.

_Proof._--Double the speed of the screw, then it strikes the air twice as hard; it also strikes twice as much air, and the motor has to go twice as fast to do it.

§ 20. To compare one model with another the formula

Weight × velocity (in ft. per sec.)/horse-power

is sometimes useful.

§ 21. =A Horse-power= is 33,000 lb. raised one foot in one minute, or 550 lb. one foot in one second.

A clockwork spring raised 1 lb. through 4½ ft. in 3 seconds. What is its h.p.?

1 lb. through 4½ ft. in 3 seconds is 1 lb. " 90 ft. " 1 minute.

{therefore} Work done is 90 ft.-lb. = 90/33000 = 0·002727 h.p.

The weight of the spring was 6¾ oz. (this is taken from an actual experiment), i.e. this motor develops power at the rate of 0·002727 h.p. for 3½ seconds only.

§ 22. =To Ascertain the H.P. of a Rubber Motor.= Supposing a propeller wound up to 250 turns to run down in 15 seconds, i.e. at a mean speed of 1200 revolutions per minute or 20 per second. Suppose the mean thrust to be 2 oz., and let the pitch of the propeller be 1 foot. Then the number of foot-pounds of energy developed

= (2 oz. × 1200 revols. × 1 ft. (pitch)) / 16 oz.

= 150 ft.-lb. per minute.

But the rubber motor runs down in 15 seconds.

{therefore} Energy really developed is

= (150 × 15) / 60 = 37·5 ft.-lb.

The motor develops power at rate of 150/33000 = 0·004545 h.p., but for 15 seconds only.

§ 23. =Foot-pounds of Energy in a Given Weight of Rubber= (experimental determination of).

Length of rubber 36 yds. Weight " 2-7/16 oz. Number of turns = 200.

12 oz. were raised 19 ft. in 5 seconds. i.e. ¾ lb. was raised 19 × 12 ft. in 1 minute. i.e. 1 lb. was raised 19 × 3 × 3 ft. in 1 minute. = 171 ft. in 1 minute.

i.e. 171 ft.-lb. of energy per minute. But actual time was 5 seconds.

{therefore} Actual energy developed by 2-7/16 oz. of rubber of 36 yards, i.e. 36 strands 1 yard each at 200 turns is

= 171/12 ft.-lb.

= 14¼ ft.-lb.

This allows nothing for friction or turning the axle on which the cord was wound. Ball bearings were used; but the rubber was not new and twenty turns were still unwound at the end of the experiment. Now allowing for friction, etc. being the same as on an actual model, we can take ¾ of a ft.-lb. for the unwound amount and estimate the total energy as 15 ft.-lb. as a minimum. The energy actually developed being at the rate of 0·0055 h.p., or 1/200 of a h.p. if supposed uniform.

§ 24. The actual energy derivable from 1 lb. weight of rubber is stated to be 300 ft.-lb. On this basis 2-7/16 oz. should be capable of giving 45·7 ft.-lb. of energy, i.e. three times the amount given above. Now the motor-rubber not lubricated was only given 200 turns--lubricated 400 could have been given it, 600 probably before rupture--and the energy then derivable would certainly have been approximating to 45 ft.-lb., i.e. 36·25. Now on the basis of 300 ft.-lb. per lb. a weight of ½ oz. (the amount of rubber carried in "one-ouncers") gives 9 ft.-lb. of energy. Now assuming the gliding angle (including weight of propellers) to be 1 in 8; a perfectly efficient model should be capable of flying eight times as great a distance in a horizontal direction as the energy in the rubber motor would lift it vertically. Now 9 ft.-lb. of energy will lift 1 oz. 154 ft. Therefore theoretically it will drive it a distance (in yards) of

(8 × 154)/3 = 410·6 yards.

Now the greatest distance that a 1 oz. model has flown in perfectly calm air (which never exists) is not known. Flying with the wind 500 yards is claimed. Admitting this what allowance shall we make for the wind; supposing we deduct half this, viz. 250 yards. Then, on this assumption, the efficiency of this "one ouncer" works out (in perfectly still air) at 61 per cent.

The gliding angle assumption of 1 in 8 is rather a high one, possibly too high; all the writer desires to show is the method of working out.

Mr. T.W.K. Clarke informs me that in his one-ouncers the gliding angle is about 1 in 5.

§ 25. =To Test Different Motors or Different Powers of the Same Kind of Motor.=--Test them on the same machine, and do not use different motors or different powers on different machines.

§ 26. =Efficiency of a Model.=--The efficiency of a model depends on the weight carried per h.p.

§ 27. =Efficiency of Design.=--The efficiency of some particular design depends on the amount of supporting surface necessary at a given speed.

§ 28. =Naphtha Engines=, that is, engines made on the principle of the steam engine, but which use a light spirit of petrol or similar agent in their generator instead of water with the same amount of heat, will develop twice as much energy as in the case of the ordinary steam engine.

§ 29.=Petrol Motors.=

Horse-power. No. of Cylinders. Weight. ¼ Single 4½ lb. ½ to ¾ " 6½ " 1½ Double 9 "

§ 30. =The Horse-power of Model Petrol Motors.=--Formula for rating of the above.

(R.P.M. = revolutions per minute.)

H.P. = ((Bore)² × stroke × no. of cylinders × R.P.M.)/12,000

If the right-hand side of the equation gives a less h.p. than that stated for some particular motor, then it follows that the h.p. of the motor has been over-estimated.

§ 30A. =Relation between Static Thrust of Propeller and Total Weight of Model.=--The thrust should be approx. = ¼ of the weight.

§ 31. =How to find the Height of an Inaccessible Object by Means of Three Observations taken on the Ground (supposed flat) in the same Straight Line.=--Let A, C, B be the angular elevations of the object D, as seen from these points, taken in the same straight line. Let the distances B C, C A and A B be _a_, _b_, _c_ respectively. And let required height P D = _h_; then by trigonometry we have (see Fig. 56)

_h²_ = _abc_/(_a_ cot²A - _c_ cot²C + _b_ cot²B).

§ 32. =Formula= for calculating the I.H.P. (indicated horse-power) of a single-cylinder double-acting steam-engine.

Indicated h.p. means the h.p. actually exerted by the steam in the cylinder without taking into account engine friction. Brake h.p. or effective h.p. is the actual h.p. delivered by the crank shaft of the engine.

I.H.P. = (2 × S × R × A × P)/33,000.

Where S = stroke in feet. R = revolutions per minute. A = area of piston in inches. P = mean pressure in lb. exerted per sq. in. on the piston.

The only difficulty is the mean effective pressure; this can be found approximately by the following rule and accompanying table.

TABLE VI.

---------+----------+---------+----------+---------+--------- Cut-off | Constant | Cut-off | Constant | Cut-off | Constant ---------+----------+---------+----------+---------+--------- 1/6 | ·566 | 3/8 | ·771 | 2/3 | ·917 1/5 | ·603 | ·4 | ·789 | ·7 | ·926 1/4 | ·659 | 1/2 | ·847 | 3/4 | ·937 ·3 | ·708 | ·6 | ·895 | ·8 | ·944 1/3 | ·743 | 5/8 | ·904 | 7/8 | ·951 ---------+----------+---------+----------+---------+---------

Rule.--"Add 14·7 to gauge pressure of boiler, this giving 'absolute steam pressure,' multiply this sum by the number opposite the fraction representing the point of cut-off in the cylinder in accompanying table. Subtract 17 from the product and multiply the remainder by 0·9. The result will be very nearly the M.E.P." (R.M. de Vignier.)

FOOTNOTE:

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

APPENDIX A.

SOME MODELS WHICH HAVE WON MEDALS AT OPEN COMPETITIONS.

The model shown in Fig. 57 has won more competition medals than any other. It is a thoroughly well designed[54] and well constructed model. Originally a very slow flyer, the design has been simplified, and although by no means a fast flyer, its speed has been much accelerated. Originally a one-propeller machine, it has latterly been fitted with twin propellers, with the idea of obtaining more directional control; but in the writer's opinion, speaking from personal observation, with but little, if any, success. The steering of the model is effected by canting the elevator. Originally the machine had ailerons for the purpose, but these were removed owing, I understand, to their retarding the speed of the machine.

In every competition in which this machine has been entered it has always gained very high marks for stability.

Up to the time of writing it has not been provided with anything in the nature of fins or rudder.

Fig. 58 is a biplane very much after the type of the model just alluded to, but the one straight and one curved aerofoil surfaces are here replaced by two parallel aerofoils set on a dihedral angle. The large size of the propeller should be noted; with this the writer is in complete agreement. He has not unfortunately seen this model in actual flight.

The scientifically designed and beautifully made models illustrated in Fig. 59 are so well known that any remarks on them appear superfluous. Their efficiency, so far as their supporting area goes, is of the highest, as much as 21 oz. per square foot having been carried.

For illustrations, etc., of the Fleming-Williams model, _see_ ch. v., § 23.

(Fig. 60.) This is another well-constructed and efficient model, the shape and character of the aerofoil surfaces much resembling those of the French toy monoplane AL-MA (see § 4, ch. vii.), but they are supported and held in position by quite a different method, a neat little device enabling the front plane to become partly detached on collision with any obstacle. The model is provided with a keel (below the centre of gravity), and rudder for steering; in fact, this machine especially claims certainty of directional control. The writer has seen a number of flights by this model, but it experiences, like other models, the greatest difficulty in keeping straight if the conditions be adverse.

The model which will do this is, in his opinion, yet to be evolved. The small size of the propellers is, of course, in total disagreement with the author's ideas. All the same, the model is in many respects an excellent one, and has flown over 300 yards at the time of writing.

More than a year ago the author made a number of models with triangular-shaped aerofoils, using umbrella ribs for the leading edge and steel piano wire for the trailing, but has latterly used aerofoils of the elongated ellipse shape.

Fig. 61 is an illustration of one of the author's latest models which won a Bronze Medal at the Long Distance Open Competition, held at the Crystal Palace on July 27, 1910, the largest and most keenly contested competition held up to that date.

The best and straightest flight against the wind was made by this model.

On the morning of the competition a flight of about 320 yards (measured in a straight line) was made on Mitcham Common, the model being launched against the wind so as to gain altitude, and then flying away with the breeze behind the writer. Duration of flight 50 seconds. The following are the chief particulars of the model:--Weight, 7½ oz. Area of supporting surface, 1-1/3 sq. ft. Total length, 4 ft. Span of main aerofoil, 25 in. Aspect ratio, 4 : 1. Diameter of propeller, 14 in. Two strand geared rubber motor, carrying altogether 28 strands of 1/16 square rubber cord 43 in. long. The propeller was originally a Venna, but with the weight reduced by one-third, and considerable alteration made in its central contours. The front skid of steel pianoforte wire, the rear of jointless cane wire tipped; the rear skid was a necessity in order to protect the delicate gearing mechanism, the weight of which was reduced to a minimum.

The very large diameter of the propeller should be noted, being 56 per cent. of the span. The fin, high above the centre of gravity, was so placed for transverse stability and direction. At the rear of the fin was a rudder. The small amount of rubber carried (for a long distance machine) should also be noted, especially when allowing for friction in gearing, etc.

The central rod was a penny bamboo cane, the large aerofoil of jointless cane and Hart's fabric, and the front aerofoil of steel wire surfaced with the same material.

LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.

FOOTNOTE:

[54] The design is patented.

_October, 1910_

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=Coffee=, its Culture and Commerce in all Countries. By C.G.W. LOCK. 11 plates, 274 pp. crown 8vo. (_1888_)

12 6

=Sugar, a Handbook for Planters and Refiners.= By the late J.A. R. NEWLANDS and B.E.R. NEWLANDS. 236 illus. 876 pp. demy 8vo. (_London, 1909_)

_net_ 1 5 0

=Hops=, their Cultivation, Commerce and Uses. By P.L. SIMMONDS. 143 pp. crown 8vo. (_1877_)

4 6

=The Future of Cocoa-Planting=. By H. HAMEL SMITH. With illustrations, 95 pp. crown 8vo, sewed. (_1908_)

_net_ 1 0

=Estate Fences=, their Choice, Construction and Cost. By A. VERNON. Re-issue, 150 illus. 420 pp. 8vo. (_1909_)

_net_ 8 6

ARCHITECTURE AND BUILDING.

=The Hydropathic Establishment and its Baths.= By R.O. ALLSOP. 8 plates, 107 pp. demy 8vo. (_1891_)

5 0

=The Turkish Bath=, its Design and Construction. By R.O. ALLSOP. 27 illus. 152 pp. demy 8vo. (_1890_)

6 0

=Public Abattoirs=, their Planning, Design and Equipment. By R.S. AYLING. 33 plates, 100 pp. demy 4to. (_1908_)

_net_ 8 6

=The Builder's Clerk.= By T. BALES. Second edition, 92 pp. fcap. 8vo. (_1904_)

1 6

=Glossary of Technical Terms= used in Architecture and the Building Trades. By G.J. BURNS. 136 pp. crown 8vo. (_1895_)

3 6

=Chimney Design and Theory.= By W.W. CHRISTIE. Second edition, 54 illus. 200 pp. crown 8vo. (_New York, 1902_)

_net_ 12 6

=Approximate Estimates.= By T.E. COLEMAN. Third edition, 481 pp. oblong 32mo, leather. (_1907_)

_net_ 5 0

=Stable Sanitation and Construction.= By T.E. COLEMAN. 183 illus. 226 pp. crown 8vo. (_1897_)

_net_ 6 0

=Architectural Examples= in Brick, Stone, Wood and Iron. By W. FULLERTON. Third edition, 245 plates, 254 pp. demy 4to. (_1908_)

_net_ 15 0

=Bricklaying System.= By F.B. GILBRETH. Fully illustrated, 321 pp. 8vo. (_New York, 1909_)

_net_ 12 6

=Field System.= By F.B. GILBRETH. 194 pp. 12mo leather. (_New York, 1908_)

_net_ 12 6

=The Building Trades Pocket Book.= Compiled by R. HALL. 12mo. With interchangeable diary

_net_ 1 6

Ditto ditto, in leather

_net_ 2 6

=The Clerk of Works' Vade Mecum.= By G.G. HOSKINS. Seventh edition, 52 pp. fcap. 8vo. (_1901_)

1 6

=A Handbook of Formulæ, Tables, and Memoranda=, for Architectural Surveyors and others engaged in Building. By J.T. HURST. Fifteenth edition, 512 pp. royal 32mo, roan. (_1905_)

_net_ 5 0

=Quantity Surveying=, for the Use of Surveyors, Architects, Engineers and Builders. By J. LEANING. Fifth edition, 936 pp. demy 8vo. (_1904_)

_net_ 1 5 0

=Obstruction to Light.= A Graphic Method of determining Problems of Ancient Lights. By H.B. MOLESWORTH. 9 folding plates, 4to. (_1902_)

_net_ 6 0

=Suburban Houses.= A series of practical plans. By J.H. PEARSON. 46 plates and 12 pp. text, crown 4to. (_1905_)

_net_ 7 6

=Solid Bitumens=, their Physical and Chemical Properties and Chemical Analysis. By S.F. PECKHAM. 23 illus. 324 pp. 8vo. (_New York, 1909_)

_net_ 1 1 0

=Roman Architecture, Sculpture and Ornament.= By G.B. PIRANESI. 200 plates, reproduced in facsimile from the original. 2 vols. Imperial folio, in wrappers. (_1900_)

_net_ 2 2 0

=The Seven Periods of English Architecture=, defined and illustrated. By E. SHARPE. Third edition, 20 steel plates, royal 8vo. (_1888_)

12 6

=Our Factories, Workshops and Warehouses=, their Sanitary and Fire-Resisting Arrangements. By B.H. THWAITE. 183 illus. 282 pp. crown 8vo. (_1882_)

9 0

=Elementary Principles of Carpentry.= By T. TREDGOLD and J.T. HURST. Eleventh edition, 48 plates, 517 pp. crown 8vo. (_1904_)

12 6

=Practical Stair Building and Handrailing.= By W.H. WOOD. 32 plates, 91 pp. crown 4to. (_1894_)

10 6

=Spons' Architects' and Builders' Pocket Price-Book=, Memoranda, Tables and Prices. Edited by CLYDE YOUNG. Revised by STANFORD M. BROOKS. Illustrated, 552 pp. 16mo, leather cloth (size 6½ in. by 3¾ in. by ½ in. thick). Issued annually

_net_ 3 0

=Heating Engineers' Quantities.= By W.L. WHITE and G.M. WHITE. 4 plates, 33 pp. folio. (_1910_)

_net_ 10 6

ARTILLERY.

=Guns and Gun Making Material.= By G. EDE. Crown 8vo. (_1889_)

6 0

=Treatise on Application of Wire to Construction of Ordnance.= By J.A. LONGRIDGE. 180 pp. 8vo. (_1884_)

1 5 0

=The Progress of Artillery: Naval Guns.= By J.A. LONGRIDGE. 8vo, sewed. (_1896_)

2 0

=The Field Gun of the Future.= By J.A. LONGRIDGE. 8vo, sewed. (_1892_)

2 6

BRIDGES, ARCHES, ROOFS, AND STRUCTURAL DESIGN.

=Strains in Ironwork.= By HENRY ADAMS. Fourth edition, 8 plates, 65 pp. crown 8vo. (_1904_)

5 0

=The Practical Designing of Structural Ironwork.= By HENRY ADAMS. 13 plates, 194 pp. 8vo. (_1894_)

8 6

=Designing Ironwork.= By HENRY ADAMS. Second series. 8vo, sewed.