[Verse 1]
Tsiolkovsky put his pen to paper, eighteen-oh-three
Said the math don't care about your feelings or your plea
Delta-v equals exhaust velocity times the log
Of your initial mass divided by the final — that's the slog
Natural logarithm, mass ratio's the key
The heavier your fuel load, the less efficient you'll be
Specific impulse measures seconds of thrust per pound
Hydrogen and oxygen — four fifty off the ground
[Chorus]
Delta-v equals vee-sub-e times el-en of m-naught over m-final
The tyranny is real, the equation is the bible
Log of mass ratio — that's the wall you gotta scale
Two to four percent makes payload, everything else is propellant trail
Mass ratio, exhaust speed, logarithm in between
Stack your stages, burn your propellant — that's the rocket machine
[Verse 2]
Nine point four kilometres per second just to circle Earth
That's the LEO tax — you pay it from the moment of your birth
Then three point two more for trans-lunar injection burn
Gravity's a creditor with interest you can't spurn
Point nine for lunar orbit insertion, slow it down
Two klicks per second more to set your lander on the ground
Add the margins, add the losses, atmospheric drag
Total delta-v budget: fifteen clicks — don't let it sag
[Chorus]
Delta-v equals vee-sub-e times el-en of m-naught over m-final
The tyranny is real, the equation is the bible
Log of mass ratio — that's the wall you gotta scale
Two to four percent makes payload, everything else is propellant trail
Mass ratio, exhaust speed, logarithm in between
Stack your stages, burn your propellant — that's the rocket machine
[Bridge]
Single stage means dragging empty tankage all the way
Drop the dead mass early, that's the staging gospel they say
Optimal split — analyse the Isp at each separation
Each stage exponential, it's a compound calculation
Falcon drops its booster, Saturn dropped its S-IC
Every empty cylinder you ditch is payload flying free
The equation doesn't bend for billionaires or governments
You cannot argue logarithms into different increments
[Verse 3]
A Saturn Five weighed three thousand tonnes upon the pad
Forty-five tonnes reached the Moon — the ratio's bleak and sad
Less than two percent survives the rocket equation's cut
That's the tyranny — the math just keeps the door half-shut
So engineers chase Isp like it's printed gold
A single second's gain in exhaust speed makes payload manifold
Methalox versus hydrolox versus kerosene debate
Every point of specific impulse compounds with your freight
[Chorus]
Delta-v equals vee-sub-e times el-en of m-naught over m-final
The tyranny is real, the equation is the bible
Log of mass ratio — that's the wall you gotta scale
Two to four percent makes payload, everything else is propellant trail
Mass ratio, exhaust speed, logarithm in between
Stack your stages, burn your propellant — that's the rocket machine