Sunday, March 26, 2006

Thrust Into Space excerpt Pg. #14

Fuel Consumption

A large thrust can be obtained by ejecting a large amount of propellant or by ejecting a small amount at a high velocity.

I(sp) = T / w

...specific impulse...

has the dimensions of time since it is thrust in pounds
divided by propellant consumption in pounds per second.

Page 14 of Maxwell W. Hunter II 's Thrust into Space
SI: from

We can divide this equation by the weight of the propellants to define the specific impulse. The word "specific" just means "divided by weight". The specific impulse Isp is given by:

Isp = Veq / g0

where g0 is the gravitational acceleration constant (32.2 ft/sec^2 in English units, 9.8 m/sec^2 in metric units). Now, if we substitute for the equivalent velocity in terms of the thrust:

Isp = F / (mdot * g0)

Mathematically, the Isp is a ratio of the thrust produced to the weight flow of the propellants. A quick check of the units for Isp shows that:

Isp = m/sec / m/sec^2 = sec

Why are we interested in specific impulse? First, it gives us a quick way to determine the thrust of a rocket, if we know the weight flow rate through the nozzle. Second, it is an indication of engine efficiency. Two different rocket engines have different values of specific impulse. The engine with the higher value of specific impulse is more efficient because it produces more thrust for the same amount of propellant. Third, it simplifies our mathematical analysis of rocket thermodynamics. The units of specific impulse are the same whether we use English units or metric units. Fourth, it gives us an easy way to "size" an engine during preliminary analysis. The result of our thermodynamic analysis is a certain value of specific impulse. The rocket weight will define the required value of thrust. Dividing the thrust required by the specific impulse will tell us how much weight flow of propellants our engine must produce. This information determines the physical size of the engine.

Excerpt #1 and links to other excerpts


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