that would be my typical glitch ... can you share the formula you would use for a 3:1 thrust to weight ratio as it relates to the units that motors/engines are specified in
The reason I said metric was easier is because the weight of a rocket is correctly reported in Newtons and our units for thrust are most commonly in Newtons. One kilogram of mass weighs 9.81 Newtons (mass times the acceleration of gravity). With a 3:1 thrust to weight ratio a rocket weighing 9.81 Newtons would require at least 29.43 Newtons of thrust.
The sum of the forces on the rocket then are thrust in the upward direction and gravity downward, or 29.43 - 9.81 = 19.62 Newtons, which is 19.62 kilogram * meters per second per second. F = mass * acceleration so one kilogram is accelerated at the rate of 19.62 meters/second squared.
When acceleration and distance are both known the formulas can be rearranged algebraically to find velocity at any given distance.
Assuming v starts at 0, acceleration ‘a’ is incremental distance ‘d’ per time ‘t’ per time -> a = d/t/t or a = d/(t^2)
Velocity ‘v’ = d/t
Express both in terms of time:
t = d/v
t^2 = d/a, so t = (d/a)^(1/2) or sqrt(d/a)
So, d/v = Sqrt(d/a)
Solve for v
v = d/(Sqrt(d/a))
A six foot rail is 1.829 meters. Plug in the numbers
v = 1.829 / Sqrt(1.829/19.62)
v = 6 meters per second or 19.65 feet per second. (I hope someone checks my algebra and basic math!!)
You can see why a 5:1 thrust to weight ratio is recommended by Tripoli in its Safety Code.