Re: Need Physics Help!

Noah Doyle wrote:
> 
> OK, in the course of trying to get my (pseudo) realistic FT rules put
to
> gether, I have run into an obstacle:	I need equations!
> I have, variously, the numbers for acceleration, distance and time.  I
may
> need to solve for any one of these.
> I need equations for:
> Rest-to-rest with constant accel/decel.
> Rest-to-point with constant accel (& vice versa: point-to-rest with
> constant decel).
> And both of those again, with only a certain amount of accel/decel
(limited
> thrust manuvers)

	Here are some equations I've managed to accumulate:

* WARNING * The below equations assume a constant acceleration,
which is not  true for a ship expending mass (for instance, 
propellant). Ai = F/Mc so as the ship's mass goes down, the acceleration
goes up 
( where Ai = "instantaneous" acceleration (m/sec^2),
F = Thrust (Newtons or kg m/sec), 
and Mc = Ship's "current" mass (at this moment in time) (kg))

============================================
When you have two out of three of 
average velocity (Va) in m/sec,
change in distance (S) in meters 
or time (T) in seconds
Va = S / T
S = Va * T
T = S / Va
============================================
When you have two out of three of 
acceleration (A) in m/sec^2,
change in velocity (V) in m/sec
or time (T) in seconds
A = V / T
V = A * T
T = V / A
============================================
When you have two out of three of 
change in distance (S) in meters,
acceleration (A) in m/sec^2, 
or time (T) in seconds
plus Initial Velocity (Vi) in m/sec 
(Note: if deaccelerating, acceleration A is negative)
S = (Vi * T) + ((A * (T^2)) / 2)
A = (S - (Vi * T)) / ((T^2) / 2)
T =  (sqrt[(Vi^2) + (2 * A * S)] - Vi) / A
If Vi = 0 then
S = (A * (T^2)) / 2
A = (2 * S) / (T^2)
T = sqrt[(2 * S) / A]
============================================
When you have two out of three of 
change in distance (S) in meters,
acceleration (A) in m/sec^2, 
or final velocity (Vf) in m/sec
plus Initial Velocity (Vi) in m/sec
(Note: if Vf < Vi, then A will be negative (deacceleration))
S = (Vf^2 - Vi^2) / (2 * A)
A = (Vf^2 - Vi^2) / (2 * S)
Vf = sqrt[Vi^2 + (2 * A * S)]
If Vi = 0 then
S = (Vf^2) / (2 * A)
A = (Vf^2) / (2 * A)
Vf = sqrt[2 * A * S]
============================================
If the ship constantly accelerates to the midpoint, then
deaccelerates to arrive with zero velocity at the 
destination:
T = 2 * sqrt[S / A]
S = (A * (T^2)) / 4
A = (4 * S) / (T^2)


I've got equations for relativistic acceleration,
but they are quite nasty.  They are available upon request.

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