Thrust = (Mass of rocket X Specific Impulse X acceleration due to gravity)
MLT(^-2) = M*T*(L / (T*T)) ? i.e MLT^(-2) != MLT^(-1)
Just a nitpick though
That is a perfectly correct equation. Just one little problem. You are assuming the dimensions on both sides to be equal. If that were the case, the unit of efficiency of a rocket engine would be, like all other engines in the world, dimensionless.
But that isn't the case is it ?
Most efficiencies that we calculate and formulate in the world are to measure how much energy was converted from one form to the other, in rocket sciences none of that matters. Its all about how much fuel you need to carry a given payload assuming the engine has a given Isp.
Needless to say this is a weird premise and it leads to some pretty outlandish assumptions. For example the "g" is always assumed to be 9.81 m/s2, irrespective of where the rocket is. You could argue that gravity reduces as you get far away from earth but the equations will always take acceleration due to gravity as 9.81. Doesn't matter if the rocket is sitting next to the Sun where the gravity is 1000 times higher, it always going to be 9.81. Seems unreasonable doesn't it ?
This whole equation is just a weird but internationally accepted assumption. Just like how we all agree that a given length is 1 meter, a given duration is 1 sec and so on. We need these assumptions to base our calculations on.
Isp is measure in seconds because no matter what system(SI, mks,fps etc) you follow, time is always in seconds. It was internationally accepted to be the standard in the 1950s and 60s, largely because the German scientists working with Americans in NASA used the metric system and the Americans used the imperial system. This caused all kinds of problems.
All these assumptions ensures pretty inaccurate outcomes, sometimes ridiculously funny. For example you can use the delta-v equation to find the speed of a rocket, however the result will be always wrong. The actual speed will be lower than the calculated figure. Back a long time ago scientists use to use these results as a reference, nowadays nobody does that.
Basing flight time on just the battery, implies the entire missile is built around the constraints of the battery.. Why not connect two of these batteries in parallel and have longer flight time..
There are constraints of space, weight etc for every missile, especially air to air missiles. Adding another battery consumes internal space which has to be compensated by reducing fuel load. This will reduce range and speed of the missile. That not an option here.
What can be done is that we make better propulsion systems and more efficient batteries in the future.
Work is already ongoing in the batteries department, we are making some very efficient zinc batteries for our upcoming heavyweight electric torpedoes.
On the propulsion front we might have hit a plateau. Boron based fuel, used by SFDR, are the most powerful among all solid fuels(google zip fuel) and any advancement in speed and range will require either making larger missiles or some breakthrough in scramjet engines.
For now let's just worry about making this thing operational first.