The equation is:
[math]\Delta v=v_{e}\cdot\ln\frac{m_{0}}{m_{1}}[/math]
Where [math]v_{e}[/math] is exhaust velocity in metres/second, not engine specific impulse [math]I_{sp}[/math] in seconds. It's confusing, because what Orbiter defines as specific impulse is actually exhaust velocity.
Actually, specific impulse and exhaust velocity are the same. What is wrong is calling the value with the unit seconds an specific impulse. It is more a specific combustion endurance.
Specific impulse, by the words is "impulse per propellant mass". Impulse is force integrated by time, which means it is measured in SI units in "Ns" or "Newton seconds". so, specific impulse is measured in "N s /kg" which, by the definition of Newtons as " kg m/s²" means, that this unit for the specific impulse is also a velocity, since the units reduce themselves to "m/s".
Specific impulse and average exhaust velocity of one or more engines, are both equivalent. They just come together from different directions.
Thrust is mass flow multiplied by exhaust velocity. Impulse is Thrust force integrated by time or, at constant thrust, thrust force multiplied by time.
I = Ve * mdot * t
Mass flow at constant thrust is total propellant mass (consumed) divided by time.
I = Ve * mp / t * t = Ve * mp
Specific impulse is (again) Impulse divided by propellant mass (consumed):
Isp = I/mp = Ve * mp/mp = Ve
Now, if the time would be infinitely small, all mass mp would be consumed instantly. There would be just a single short impulse (like an explosion) and the velocity would be changed by:
dv [m/s]= (I[Ns]/m0 [kg]) [kg m s/(kg s²)]
But the reality is not like that. Instead, it is a sum of many infinitely small impulses, with the rocket getting lighter with every impulse. The lighter the rocket gets, the more velocity is gained by every (constant) impulse. That reality is described with the rocket equation.
---------- Post added at 05:25 PM ---------- Previous post was at 05:23 PM ----------
since the number can accurately represent the number of seconds the rocket can hover in the air.
One more fallacy that should be added to the list of reasons why specific impulse should never ever be measured in seconds again.
Can a rocket with a specific impulse of 350 seconds hover its own mass for 350 seconds? Sure not without quite many other conditions to be fullfilled, so that the claim works out.
