I've been crunching numbers and I hit a snag.... (fuel flow)

[RedKosmos]

Ok, so I've been playing for a few months now and I have finally decided to incorporate math into my ship designs (before I just eye-balled it). I started with fuel spent per second, however, I did all my tests stationary (on the lift-off clamps) and now that I'm doing flight tests none of my numbers match up. The fuel flow rate as my rocket ascends, decreases. What is causing this? How can I plug this into my math? I'm trying to make different fuel tank/engine combinations share the same burn time. For example, a 2160u fuel tank with a Skipper and a 180u fuel tank with a LV-N. Math is NOT my strong point (the reason why I'm doing this is to learn and practice), so please explain it simple. Thanks for reading my post!

[Rhomphaia]

ISP increases as atmospheric pressure decreases. In KSP this is modeled with a change in fuel flow rate while thrust remains constant (Other way around in the real world).

Pressure can be calculated for a Given altitude

Pressure = e^(-Altitude/ScaleHeight)

For Kerbin the Scale Height is 5000m

IIRC the Value of ISP increases linearly between a pressure of 1 and 0.

ISP won't get any lower at pressures greater than 1 though

Edited September 3, 2013 by Rhomphaia

[Dangerous_Beans]

wouldn't the burn time be the Dv of the stage, divided by the average acceleration?

so for a jumbo tank with a mainsail in a vacuum, Dv = 330*9.81*ln(42/10)=4,645.8 and average acceleration would be (1500/42+1500/10)/2=92.8m/s/s, so that gives a burn time of 4645.8/92.8=50s

swap out the mainsail for an LV-N and you get 14,217m/s Dv, with an average acceleration of 5.58m/s for a burn time of ~2,548s, about 2/3rds of an hour.

Where did i go wrong?