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🚀About test launch bonuses🚀

Aa TAHA_F20

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Aa_TahaF20
I have been asking myself the question for a short time: From how many test launch bonuses can we accelerate the return of the rocket to 10 minutes and then immediately⏰️.
For those who would like to do the calculation, thank you in advance
 
I have been asking myself the question for a short time: From how many test launch bonuses can we accelerate the return of the rocket to 10 minutes and then immediately⏰️.
For those who would like to do the calculation, thank you in advance
It might be too early for me to be doing math, but..... the answer is >30. Best to use some QLs.
Below: 15% additional reduction in rocket flight time for each additional TL (calculated minutes for <1 hr flight time)
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If you care for some maths…
each TL reduces 15%, meaning the launch time will be 85% of whatsoever was before
one day has 86400 seconds
for sake of simplicity let’s assume that “instantly” means 1 sec (in practical terms there are no differences, it’s less that the time the launch animation takes, but you could measure the time for the launch animation and use that value, I guess it would be 5 to 10 secs)
then you’re looking for the value x that solves
86400 * 0.85^x = 1
solving this you get
x= - ln(86400)/ln(0.85) = 69.9
69 TL will result in around 1.1 sec launch, 70 just below 1 sec

if you’re good with a 5 min (300 seconds) launch, then you’ll be needing half the TL:
86400 * 0.85^x = 300
results in
x=(ln(300)-ln(86400))/ln(0.85) = 34.8
ie 34 for just a bit over 5 min and 35 to get under 5 min

edited: I saw later you mentioned a 10 min launch, adjusting equations above will lead to around 30 (30 above 10 min, 31, just below)
 
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