# Specific Impulse

One measure of the effectiveness of a rocket motor or fuel combination is Specific Impulse or S. I. One way to define it is (thrust x burn time)/(total mass of fuel burnt). Another way is the thrust obtained from each lb (or kg) of fuel burned each second.

In modern units, S. I. would be quoted in Ns/kg – which turns out to be dimensionally equivalent to m/s. This is because S. I. can also shown to be the same as the exhaust velocity of the gases from the combustion chamber. Furthermore, the final velocity of a rocket (in the absence of gravity, air resistance and so on) can be shown to be:

vfinai = vexhaust x ln(mass at start/mass at end)

Hence the greater the exhaust velocity, the greater the final velocity of the rocket (ignoring all the complications such as gravity, air resistance and so on).

The difference between the mass at the start and the mass at the end is effectively the mass of fuel (unless anything is jettisoned along the way!). The skill of the designer is to build a vehicle as structurally efficient as possible – all fuel and no structure is not possible, but the structural mass must be as small as possible. Blue Streak had an unusual tank structure, being a lightweight stainless steel ‘balloon’, which needed to be constantly pressurised to keep its structural integrity. Black Knight and Black Arrow were also structurally very efficient.

The equation above only applies in ideal circumstances. The effectiveness of a rocket motor is decreased in the atmosphere, since the thrust from a rocket engine derives from the pressure difference between the pressure inside the combustion chamber and the pressure outside. In a vacuum there is no outside pressure. Another way of looking at this is to say that the exhaust velocity is reduced by the air outside. Thus S. I. is sometimes quoted at sea level and sometimes in vacuum. Vacuum S. I. is typically 10-15% higher than sea level.

The HTP/kerosene combination has a relatively low S. I., around 210-220 at sea level. Oxygen/kerosene gives an S. I. of around 245 at sea level. Hydrogen/oxygen is the most effective combination of all, some motors reaching S. I.s of at least 400. One way of looking at this is to say that there is double the thrust for the same weight of fuel.