The units here are seconds, which is a bit unusual. Seconds of what, exactly? Sometimes cancelling units gives you an unexpectedly simple result, like how you can measure gas mileage in square meters. Sometimes this gives you a new, interesting interpretation of the value.
This is not the case for specific impulse.
How do you measure specific impulse? You take your engine and run it for a while. As it runs, you measure how much thrust it produces: the force it exerts. You also measure how much propellant it's consuming per second. Here's an example. We'll use the metric system.
You run your rocket for 10 seconds. In those 10 seconds, the engine used 20kg of propellant. So the engine consumed an average of 20kg/10s = 2kg/s. You measured the average thrust of the engine as 4000 Newtons. So the specific impulse of this engine is 4000N/(2kg/s) = 2000N/(kg/s).
The units here are N/(kg/s), which should make sense. It's exactly what we measured: how many Newtons of thrust the engine produces for each kilo of propellant it needs every second. If you want more thrust, you could maybe have two copies of the engine on your rocket, producing twice as much thrust. But then they would both be consuming propellant, so your consumption of propellant would double too. The specific impulse would stay constant.
We can bring the seconds to the top to get Ns/kg. This is maybe a bit less clear, but it's also a useful interpretation. Ns is a measure of impulse, or change in momentum. This is mostly what rocket scientists care about. For a rocket to perform a certain maneuver, it needs to change its velocity by a certain amount. That velocity, multiplied by the mass of the rocket, is the impulse required for the maneuver. Specific impulse tells you how much propellant you'll need to consume to get that given impulse. The "specific" in "specific impulse" means "per amount of stuff", like how specific heat capacity (measured in J/(kg*°C), or Joules per kilogram per degree Celcius) measures how much heat a substance needs to increase in temperature, per unit mass of that material. Specific impulse measures how much impulse you can get out of your propellant, per unit mass of propellant.
In base units, the Newton is kg*m/s². If we replace the Newton with its base units we get
Ns/kg = (kg*m/s²)*s/kg = (kg*m/s)/kg = m/s
So specific impulse is measured in meters per second. Is there an interesting interpretation of these units? Why yes, there is!
This is the effective exhaust velocity of the engine. It's how fast the propellant is going when it leaves the engine. The faster the propellant is travelling, the more momentum a given amount of propellant gives your rocket.
I think that's pretty cool. We never measured the exhaust velocity directly. We didn't watch the exhaust gases and see how fast they're going. It just turns out that the thing we care about — how much propellant we need to feed the engine to give our rocket a given kick — is the same as the exhaust velocity.
Using specific impulse is easy. Let's say you know you need 4000Ns of impulse, and your engine has a specific impulse of 2000m/s.
Have:That's easy.
- Required impulse: 4000Ns = 4000kg*m/s
- Specific impulse of engine: 2000m/s
Need:
- Fuel required (kg)
(4000kg*m/s) / (2000m/s) = 2kg
m/s is the true unit for specific impulse, and exhaust velocity is its cool interpretation.
So, your engine consumed 40lb/10s = 4lb/s of propellant. Its specific impulse is 800lb/(4lb/s) = 200lb/(lb/s). That is, your engine produces 200 pounds of thrust for every pound of fuel it uses per second. You cancel out the lb from the top and bottom and you get a specific impulse of 200s.
When you're using this number, everything seems fine. Say you know you're going to need 1000lb·s of impulse, (like in the metric system, you can measure impulse in the imperial system with units of force * time). and you're using that engine with a specific impulse of 200s.
Have:You divide by 200s, the specific impulse of your engine, and you see that you'll need 5lb of fuel for that maneuver.
- Required impulse: 1000lb*s
- Specific impulse of engine: 200s
Need:
- Fuel required (lb)
A metric rocket scientist comes along and asks for your specific impulse number. You tell them it's 200s. The metric scientist is aware that you two use different units, and knows to convert the numbers before plugging them in. But seconds are one of the few units you two have in common, and that's the only thing present here. No conversion needed. So the metric scientist goes off to do their calculations. Their rocket is going to do a maneuver requiring 4000Ns of impulse, and they need to know how many kilograms of propellant they'll need. So they take your specific impulse number and they... uhm... they...
Have:What?
- Required impulse: 4000Ns = 4000kg*m/s
- Specific impulse of engine: 200s
Need:
- Fuel required (kg)
Unbeknownst to the metric scientist, there's a secret imperialism in the value they were given. When the imperial scientist calculated that value, they cancelled out pounds from the top and bottom of their fraction. But those two pounds were different pounds! On top was pounds force, but on the bottom was pounds mass. You can't just cancel these out! They're not just different quantities, like feet vs miles; they represent completely different types of things!
There is a sensible way of doing things as the imperial scientist: instead of measuring thrust in pounds, you measure it in poundals (pdl), which is a lb*ft/s². This way, all the units cancel just like they do in the metric system. Your rocket consumes 40lb of fuel in 10s and produces 24'000pdl of thrust, so its specific impulse is
24'000pdl/(40lb/10s) = (24'000lb*ft/s²)/(4lb/s) = 6'000ft/s.
What a perfectly sensible unit!