# Numerical questions

The student may be surprised to find that in some of the examples below, we have used unfamiliar units such as knots for air speed and feet for altitude. This is quite deliberate, because flying is an international activity, and it is standard practice to use knots and feet for performance calculations. Anyone therefore who is thinking of making a career in aeronautics, whether as a pilot, an engineer, a technician or working in the area of flight management will have to get used to using these units and develop a feel for the magnitudes involved. Note that it is usually safer to convert the values to SI units before making calculations as these units are much simpler to use. Do not however forget to convert the answers back where appropriate. For convenience, we have given the necessary conversion factors below. You will soon get used to converting knots tom/s. You may not need to convert the feet to metres in all cases, because often all you need to know is what the relative density is at the given height. This can be found from Fig. 2.2 which gives the relative density against height, both in metres and feet.

In Europe, it is now common practice to use SI units for aerodynamic analysis and design, and for general scientific work, so questions of this type are in SI units.

It is recognised that in order to solve some of the examples, assumptions must be made which can hardly be justified in practice, and that these assumptions may have an appreciable effect on the answers. However, the benefit of solving these problems lies not in the numerical answers but in the considerations involved in obtaining them.

Unless otherwise specified, the following values should be used –

Density of water = 1000 kg/m3 Specific gravity of mercury = 13.6 Specific gravity of methylated spirit = 0.78 International nautical mile = 1852 m, or approx 6076 ft 1 knot = 0.514 m/s 1 ft = 0.3048 m

Radius of earth = 6370 km Diameter of the moon = 3490 km Distance of the moon from the earth = 385 000 km Aerofoil data as given in Appendix 1 CD for flat plate at right angles = 1.2 cylinder = 0.6 streamline shape = 0.06 pitot tube =1.00

Take the maximum length in the direction of motion for the length L in the Reynolds Number formula.

At standard sea-level conditions – Acceleration of gravity = 9.81 m/s[11] [12]

Atmospheric pressure = 101.3 kN/m2, or 1013 mb, or 760mmHg Density of air = 1.225 kg/m[13] [14] at 1013 mb and 288°K Speed of sound = 340 m/s = 661 knots = 1225 km/h Dynamic viscosity of air (//) = 17.894 X 1026kg/ms For low altitudes one millibar change in pressure is equivalent to 30 feet change in altitude.

International standard atmosphere as in Fig. 2.2.

[1] m in 5 seconds, then the power is 20 Nm (20 joules) in 5 seconds, or 4 joules per second. A joule per second (J/s) is called a watt (W), the unit of power. So the power used in this example is 4 watts. Readers who have studied electricity will already be familiar with the watt as a unit of electrical power; this is just one example of the general trend towards the realisation that all branches of science are inter-related. Note the importance of the time taken, i. e. of the rate at which the work is done; the word power or powerful, is apt to give an impression of size and brute force. The unit of 1 watt is small for practical use, and kilowatts are more often used. The old unit of a horse-power was never very satisfactory but, as a matter of interest, it was the equivalent of 745.7 watts (Fig. IB).

A body is said to have energy if it has the ability to do work, and the amount of energy is reckoned by the amount of work that it can do. The units of energy will therefore be the same as those of work. We know that petrol can do work by driving a car or an aeroplane, a man can do work by propelling a bicycle or even by walking, a chemical battery can drive an electric motor which can do work on a train, an explosive can drive a shell at high speed from the muzzle of a gun. All this means that energy can exist in many forms,

These three terms are used frequently in mechanics, so we must understand their meaning. This is especially important because they are common words too in ordinary conversation, but with rather different shades of meaning.

A force is said to do work on a body when it moves the body in the direction in which it is acting, and the amount of work done is measured by the product of the force and the distance moved in the direction of the force. Thus if a force of 10 newtons moves a body 2 m (along its line of action), it does 20 newton metres (Nm) of work. A newton metre, the unit of work, is called a joule (J). Notice that, according to mechanics, you do no work at all if you push something without succeeding in moving it – no matter how hard you push or for how long you push. Notice that you do no work if the body moves in the opposite direction, or even at right angles to the direction in which you push. Someone else must be doing some pushing – and some work!

Power is simply the rate of doing work. If the force of 10 N moves the body