ISP in 1, 2, 3

Thrust and Specific Impulse are the two most meaningful measures of a rocket engine. Thrust is easy to understand, and its units convey an idea about how more thrust can lift more payload. I_sp, on the other hand, has a confusing unit that most people use to measure time. Therefore, many people expect explainations about what I_sp is to begin with "The time it takes to...", and in fact many people do try to contrive explanations in that format. Such explanations are not only confusing, they is also useless. When a rocket scientist talks to another rocket scientist about I_sp, he is interested in conveying information about how efficient the engine is, and that efficiency is the mostly reflected in a single property: the speed that the exhaust mass leaves the engine. Physicists refer to the amount of energy put into moving something as impulse, and rocket scientists divide that total amount of energy by the mass of propellent expelled to impart that energy. This is the specific impulse. Conveniently, the value of the specific impulse of a rocket engine is the speed of the exhaust mass being expelled from that engine, so that will be our focus.

I_sp is a measure of speed, not time, even though its units are seconds.
Germans and Americans disagree on which units to use to measure distance (meters vs feet), but agree that the second is a good unit to measure time.
Acceleration, and therefore gravity in a specific place, is measured as speed divided by time in any units.

1 foot is about 0.3 meters. One meter is about 3.3 feet. Given an exhaust speed measured at 1000 meters per second, Americans want to hear that it was 3300 feet per second. If a spec call for 3000 feet per second, Germans want to read the spec as 900 meters per second. Can we invent a unit to make them both unhappy?

Gravty accelerates objects in freefall. The Germans will tell you that the gravitational acceleration of the Earth near its surface is 9.81 meters per second, every second. Americans will tell you that the gravitational acceleration of the Earth near its surface is 32.19 feet per second, every second. So after two seconds of freefall, the German expects his bratwurst to travel at 19.62 m/s and the American expects his hamburger to travel at 64.38 f/s. That's the exact same speed in different units.

Now comes the magic.

If the German divides the speed of his lunch by the value of the Earth's gravitational acceleration, both in his own units, he gets:

19.62 m/s       2
----------  =  ------  =  2 s
 9.81 m/ss      1 1/s

If the American divides the speed of his lunch by the value of the Earth's gravitational acceleration, both in his own units, he gets:

64.38 f/s       2
----------  =  ------  =  2 s
32.19 f/ss      1 1/s

They both agree on the value of 2 seconds! Not coincidentally, this value is the amount of time their respective meals were airborne. That's pretty much the definition of dividing speed by acceleration, and an operation every first-year physics student has been doing since Newton first described the relationship between gravity, time, and speed.

That last observation may lead to an answer to the question "What is I_sp" in the form of "The time it takes to...". Do you see it? Stop here if you want to think about it for a little bit, because the answer is in the next paragraph.

An intuitive and relevant answer to the question "What is I_sp" could be: The time it takes for a freefalling object to reach the speed of the exhaust mass of this engine. Could you imagine the speed of a bratwurst falling for over six minutes?

Date Published: 2020-09-08