The Theory and Practice of Model Aeroplaning Part 18

{therefore} Energy really developed is

= (150 15) / 60 = 375 ft.-lb.

The motor develops power at rate of 150/33000 = 0004545 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. 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.

= 14 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 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 00055 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 457 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. 3625. Now on the basis of 300 ft.-lb. per lb. a weight of oz. (the amount of rubber carried in "one-ouncers") gives 9 ft.-lb. of energy. Now a.s.suming 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 = 4106 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 a.s.sumption, the efficiency of this "one ouncer" works out (in perfectly still air) at 61 per cent.

The gliding angle a.s.sumption 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.

Single 4 lb.

to " 6 "

1 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) 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.

[Ill.u.s.tration: FIG. 56.]

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

_h_ = _abc_/(_a_ cotA - _c_ cotC + _b_ cotB).

-- 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 147 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 09.

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 COMPEt.i.tIONS.