Mass weight and g

The mass of a body depends on the amount of matter in it, and it will not vary with its position on the earth, nor will it be any different if we place it on the moon. The weight (the force due to gravity) will change, however, because the so-called gravity constant will be different on the moon, due to the smaller mass of the moon, and will even vary slightly between different points on the earth. Also, therefore, the rate at which a falling object accelerates will be dif­ferent. On the moon it will fall noticeably slower, as can be observed in the apparently slow-motion moon-walking antics of the Apollo astronauts.

Units

The system of units that we use to measure quantities, feet, metres, etc., can be a great source of confusion. In European educational establishments and most of its industry, a special form of the metric system known as the Systeme International or SI is now in general use. The basic units of this system are the kilogram for mass (not weight) (kg), the metre for distance (m) and the second for time (s).

Temperatures are in degrees Celsius (or Centigrade) (°С) when measured relative to the freezing point of water, or in Kelvin (K) when measured relative to absolute zero; 0°C is equivalent to 273 K. A temperature change of one degree Centigrade is exactly the same as a change of one degree Kelvin, it is just the starting or zero point that is different. Note that the degree symbol ° is not used when temperatures are written in degrees Kelvin, for example we write 273 K.

Forces and hence weights are in newtons (N) not kilograms. Beware of weights quoted in kilograms; in the old (pre-SI) metric system still commonly used in parts of Europe, the name kilogram was also used for weight or force. To convert weights given in kilograms to newtons, simply multiply by 9.81.

The SI system is known as a coherent system, which effectively means that you can put the values into formulae without having to worry about conver­sion factors. For example, in the expression relating force to mass and acceleration: F = m X a, we find that a force of 1 newton acting on a mass of 1 kilogram produces an acceleration of 1 m/s2. Contrast this with a version of the old British ‘Imperial’ system where a force of 1 pound acting on a mass of 1 pound produces an acceleration of 32.18 ft/sec2. You can imagine the prob­lems that the latter system produces. Notice how in this system, the same name, the pound, is used for two different things, force and mass.

Because aviation is dominated by American influence, American Federal units and the similar Imperial (British) units are still in widespread use. Apart from the problem of having no internationally agreed standard, the use of Federal or Imperial units can cause confusion, because there are several alternative units within the system. In particular, there are two alternative units for mass, the pound mass, and the slug (which is equivalent to 32.18 pounds mass). The slug may be unfamiliar to most readers, but it is commonly used in aeronautical engineering because, as with the SI units, it produces a coherent system. A force of 1 pound acting on a mass of one slug produces an acceleration of 1 ft/sec2. The other two basic units in this system are, as you may have noticed, the foot and the second. Temperatures are measured in degrees Fahrenheit.

You may find all this rather confusing, but to make matters worse, in order to avoid dangerous mistakes, international navigation and aircraft operations conventions use the foot for altitude, and the knot for speed. The knot is a nautical mile per hour (0.5145 m/s). A nautical mile is longer than a land mile, being 6080 feet instead of 5280 feet. Just to add a final blow, baggage is nor­mally weighed in kilograms (not even newtons)!

To help the reader, most of the problems and examples in this book are in SI units. If you are presented with unfamiliar units or mixtures of units, convert them to SI units first, and then work in SI units. One final tip is that when working out problems, it is always better to use basic units, so convert millimetres or kilometres to metres before applying any formulae. In the real world of aviation, you will have to get used to dealing with other units such as slugs and knots, but let us take one step at a time. Below, we give a simple example of a calculation using SI units (see Example 1.1).

EXAMPLE 1.1

The mass of an aeroplane is 2000 kg. What force, in addition to that required to overcome friction and air resistance, will be needed to give it an accelera­tion of 2 m/s2 during take-off?

SOLUTION Force = ma

= 2000 X 2 = 4000 newtons

This shows how easy is the solution of such problems if we use the SI units.

Many numerical examples on the relationship between forces and masses involve also the principles of simple kinematics, and the reader who is not familiar with these should read the next paragraph before he tackles the examples.