CHAPTER XIV.

USEFUL NOTES, TABLES, FORMULÆ, ETC.

§ 1. Comparative velocities. § 2. Conversions. § 3. Areas of various shaped surfaces. § 4. French and English measures. § 5. Useful data. § 6. Table of equivalent inclinations. § 7. Table of skin friction. § 8. Table I. (metals). § 9. Table II. (wind pressures). § 10. Wind pressure on various shaped bodies. § 11. Table III. (lift and drift) on a cambered surface. § 12. Table IV. (lift and drift)--On a plane aerofoil--Deductions. § 13. Table V. (timber). § 14. Formula connecting weight lifted and velocity. § 15. Formula connecting models of similar design but different weights. § 16. Formula connecting power and speed. § 17. Propeller thrust. § 18. To determine experimentally the static thrust of a propeller. § 19. Horse-power and the number of revolutions. § 20. To compare one model with another. § 21. Work done by a clockwork spring motor. § 22. To ascertain the horse-power of a rubber motor. § 23. Foot-pounds of energy in a given weight of rubber--Experimental determination of. § 24. Theoretical length of flight. § 25. To test different motors. § 26. Efficiency of a model. § 27. Efficiency of design. § 28. Naphtha engines. § 29. Horse-power and weight of model petrol motors. § 30. Formula for rating the same. § 30A. Relation between static thrust of propeller and total weight of model. § 31. How to find the height of an inaccessible object (kite, balloon, etc.). § 32. Formula for I.H.P. of model steam engines 125

APPENDIX A. Some models which have won medals at open competitions 143

GLOSSARY OF TERMS USED IN MODEL AEROPLANING.

_Aeroplane._ A motor-driven flying machine which relies upon surfaces for its support in the air.

_Monoplane_ (single). An aeroplane with one pair of outstretched wings.

_Aerofoil._ These outstretched wings are often called aerofoil surfaces. One pair of wings forming one aerofoil surface.

_Monoplane_ (double). An aeroplane with two aerofoils, one behind the other or two main planes, tandem-wise.

_Biplane._ An aeroplane with two aerofoils, one below the other, or having two main planes superposed.

_Triplane._ An aeroplane having three such aerofoils or three such main planes.

_Multiplane._ Any such machine having more than three of the above.

_Glider._ A motorless aeroplane.

_Helicopter._ A flying machine in which propellers are employed to raise the machine in the air by their own unaided efforts.

_Dihedral Angle._ A dihedral angle is an angle made by two surfaces that do not lie in the same plane, i.e. when the aerofoils are arranged V-shaped. It is better, however, to somewhat extend this definition, and not to consider it as necessary that the two surfaces _do_ actually meet, but would do so if produced thus in figure. BA and CD are still dihedrals, sometimes termed "upturned tips."

_Span_ is the distance from tip to tip of the main supporting surface measured transversely (across) the line of flight.

_Camber_ (a slight arching or convexity upwards). This term denotes that the aerofoil has such a curved transverse section.

_Chord_ is the distance between the entering (or leading) edge of the main supporting surface (aerofoil) and the trailing edge of the same; also defined as the fore and aft dimension of the main planes measured in a straight line between the leading and trailing edges.

span _Aspect Ratio_ is ----- chord

_Gap_ is the vertical distance between one aerofoil and the one which is immediately above it.

(The gap is usually made equal to the chord).

_Angle of Incidence._ The angle of incidence is the angle made by the chord with the line of flight.

_Width._ The width of an aerofoil is the distance from the front to the rear edge, allowing for camber.

_Length._ This term is usually applied to the machine as a whole, from the front leading edge of elevator (or supports) to tip of tail.

_Arched._ This term is usually applied to aerofoil surfaces which dip downwards like the wings of a bird. The curve in this case being at right angles to "camber." A surface can, of course, be both cambered and arched.

_Propeller._ A device for propelling or pushing an aeroplane forward or for raising it vertically (lifting screw).

_Tractor Screw._ A device for pulling the machine (used when the propeller is placed in the front of the machine).

_Keel._ A vertical plane or planes (usually termed "fins") arranged longitudinally for the purposes of stability and steering.

_Tail._ The plane, or group of planes, at the rear end of an aeroplane for the purpose chiefly of giving longitudinal stability. In such cases the tail is normally (approx.) horizontal, but not unfrequently vertical tail-pieces are fitted as well for steering (transversely) to the right or left, or the entire tail may be twisted for the purpose of transverse stability (vide _Elevator_). Such appendages are being used less and less with the idea of giving actual support.

_Rudder_ is the term used for the vertical plane, or planes, which are used to steer the aeroplane sideways.

_Warping._ The flexing or bending of an aerofoil out of its normal shape. The rear edges near the tips of the aerofoil being dipped or tilted respectively, in order to create a temporary difference in their inclinations to the line of flight. Performed in conjunction with rudder movements, to counteract the excessive action of the latter.

_Ailerons_ (also called "righting-tips," "balancing-planes," etc.). Small aeroplanes in the vicinity of the tips of the main aerofoil for the purpose of assisting in the maintenance of equilibrium or for steering purposes either with or without the assistance of the rudder.

_Elevator._ The plane, or planes, in front of the main aerofoil used for the purpose of keeping the aeroplane on an even keel, or which cause (by being tilted or dipped) the aeroplane to rise or fall (vide _Tail_).

MODEL AEROPLANING

INTRODUCTION.

§ 1. Model Aeroplanes are primarily divided into two classes: first, models intended before all else to be ones that shall _fly_; secondly, _models_, using the word in its proper sense of full-sized machines. Herein model aeroplanes differ from model yachts and model locomotives. An extremely small model locomotive _built to scale_ will still _work_, just as a very small yacht built to scale will _sail_; but when you try to build a scale model of an "Antoinette" monoplane, _including engine_, it cannot be made to fly unless the scale be a very large one. If, for instance, you endeavoured to make a 1/10 scale model, your model petrol motor would be compelled to have eight cylinders, each 0·52 bore, and your magneto of such size as easily to pass through a ring half an inch in diameter. Such a model could not possibly work.[1]

_Note._--Readers will find in the "Model Engineer" of June 16, 1910, some really very fine working drawings of a prize-winning Antoinette monoplane model.

§ 2. Again, although the motor constitutes the _chief_, it is by no means the sole difficulty in _scale_ model aeroplane building. To reproduce to scale at _scale weight_, or indeed anything approaching it, _all_ the _necessary_--in the case of a full-sized machine--framework is not possible in a less than 1/5 scale.

§ 3. Special difficulties occur in the case of any prototype taken. For instance, in the case of model Blériots it is extremely difficult to get the centre of gravity sufficiently forward.

§ 4. Scale models of actual flying machines _that will fly_ mean models _at least_ 10 or 12 feet across, and every other dimension in like proportion; and it must always be carefully borne in mind that the smaller the scale the greater the difficulties, but not in the same proportion--it would not be _twice_ as difficult to build a ¼-in. scale model as a ½-in., but _four_, _five_ or _six_ times as difficult.

§ 5. Now, the _first_ requirement of a model aeroplane, or flying machine, is that it shall FLY.

As will be seen later on--unless the machine be of large size, 10 feet and more spread--the only motor at our disposal is the motor of twisted rubber strands, and this to be efficient requires to be long, and is of practically uniform weight throughout; this alone alters the entire _distribution of weight_ on the machine and makes:

§ 6. "=Model Aeroplaning an Art in itself=," and as such we propose to consider it in the following pages.

We have said that the first requisite of a model aeroplane is that it shall fly, but there is no necessity, nor is it indeed always to be desired, that this should be its only one, unless it be built with the express purpose of obtaining a record length of flight. For ordinary flights and scientific study what is required is a machine in which minute detail is of secondary importance, but which does along its main lines "_approximate_ to the real thing."

§ 7. Simplicity should be the first thing aimed at--simplicity means efficiency, it means it in full-sized machines, still more does it mean it in models--and this very question of simplicity brings us to that most important question of all, namely, the question of _weight_.

FOOTNOTE:

[1] The smallest working steam engine that the writer has ever heard of has a net weight of 4 grains. One hundred such engines would be required to weigh one ounce. The bore being 0·03 in., and stroke 1/32 of an inch, r.p.m. 6000 per min., h.p. developed 1/489000 ("Model Engineer," July 7, 1910). When working it hums like a bee.