Hey everyone, I recently have been sucked into this game, and I'm loving the math. My question is this simple, determine the altitude a rocket will achieve on full fuel burn of a single stage. I've done a lot of research and have come up with the following example problem to test my algorithm/process of calculation. Let me know what you guys think of below and what I'm missing or potentially a force I haven't considered into the calculation such as lift, as you'll see my answer is off by nearly 3,300m. (For the sake of simplicity the rocket travels straight up in a vertical dimension only.)

Known Values of my Rocket:

Full Mass [M_{Full}] (Entire Rocket) : 7.5t (7,500kg)

Empty Mass [M_{Empty}] (First Stage Depleted) : 4.5t (4,500kg)

Fuel Mass [M_{Fuel}] (Both LQ and OX) : 3.0t (3,000kg)

Isp [I_{sp}] (Reliant Engine) : 265 sec

Thrust [F_{T}] (Thrust Force Atm.) : 205.2kN (205,200N)

LQ Rate [B_{LQ}] (Burn Rate of LQ) : 7.105 u/sec

OX Rate [B_{OX}] (Burn Rate of OX) : 8.684 u/sec

LQ Volume [V_{LQ}] (LQ Fuel 45% Mix) : 270 u

OX Volume [V_{OX}] (OX Fuel 55% Mix) : 330 u

Known Values of Kerbin:

Accel. Kerbin [g] (Accel. of Gravity) : 9.81 m/sec^2

First I will calculate the time required to burn through the fuel mixture. This time will be needed in the final calculation.

So in the end this calculation results in an effective altitude of 12,673.98 meters. If anything, I expect drag (if simulated) among other forces to take away from this value. Instead the opposite occurred, my actual test flight while holding steady to the center of the NavBall resulted in roughly 16,000 meters altitude at 38 seconds into flight (after stage finished burning).

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## BattleReadyKen

Hey everyone, I recently have been sucked into this game, and I'm loving the math. My question is this simple, determine the altitude a rocket will achieve on full fuel burn of a single stage. I've done a lot of research and have come up with the following example problem to test my algorithm/process of calculation. Let me know what you guys think of below and what I'm missing or potentially a force I haven't considered into the calculation such as lift, as you'll see my answer is off by nearly 3,300m. (For the sake of simplicity the rocket travels straight up in a vertical dimension only.)

Known Values of my Rocket:_{Full}] (Entire Rocket) : 7.5t (7,500kg)_{Empty}] (First Stage Depleted) : 4.5t (4,500kg)_{Fuel}] (Both LQ and OX) : 3.0t (3,000kg)_{sp}] (Reliant Engine) : 265 sec_{T}] (Thrust Force Atm.) : 205.2kN (205,200N)_{LQ}] (Burn Rate of LQ) : 7.105 u/sec_{OX}] (Burn Rate of OX) : 8.684 u/sec_{LQ}] (LQ Fuel 45% Mix) : 270 u_{OX}] (OX Fuel 55% Mix) : 330 uKnown Values of Kerbin:First I will calculate the time required to burn through the fuel mixture. This time will be needed in the final calculation.T=_{burn}_{}V_{LQ}/_{}B_{LQ}=_{}V_{OX }/ B_{OX}<< >> 270u / (7.105u/sec) =38.0 secNext I convert burn rate units from volume/sec to units of kg/sec. (I assume 1u = 5kg of both LQ and OX)B= B_{LQ_M}_{LQ }* (5kg/u) << >> (7.105u/sec) * (5kg/u) =35.525 kg/secB= B_{OX_M }_{OX}* (5kg/u) << >> (8.684u/sec) * (5kg/u) =43.42 kg/secB= B_{TOTAL}_{LQ}+ B_{OX}<< >> 35.525kg/sec + 43.42kg/sec =78.945 kg/sec (M *Dot = Mass Flow Rate)Determine effective exhaust velocity of rocket motor related to Specific Impulse and Gravity. (NASA Formula)V= I_{e}_{sp}* g << >> 265sec * 9.81m/sec^2 =2,599.65 m/sDetermine acceleration of rocket (Found this formula on a physics forum, not sure if valid)a= V_{e}( B_{TOTAL }/ M_{FULL}) - g << >> 2,599.65 m/s * (78.945kg/sec / 7,500kg) - 9.81m/s^2 =17.554 m/s^2Apply classical kinematic physics equation for displacement with acceleration. (Vertical Axis only...)deltaX= 0.5 * a * (T_{burn}^2) << >> 0.5 * 17.554m/s^2 * (38sec ^ 2) =12,673.988mSo in the end this calculation results in an effective altitude of

12,673.98 meters. If anything, I expect drag (if simulated) among other forces to take away from this value. Instead the opposite occurred, my actual test flight while holding steady to the center of the NavBall resulted in roughly16,000 meters altitude at 38 seconds into flight(after stage finished burning).Any ideas?

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