Firstly, I know questions like this one have already been made both in and out of the forums before, yet every thread I found and read do not fix my problem or give me an idea of what I'm doing wrong. Also, sorry if this ends up a bit too long and technical, I want to try and make it as clear and detailed as possible, especially when explaining the math I did, so it doesn't confuse or give the reader a headache.

So... I finally decided to play KSP [more] seriously, disabling "revert flight" and trying to calculate the rocket performance and everything else before launch to minimize failures. I'm playing the Enhanced Version for the Xbox, which should be pretty much a 1.2 stock for PC.

The rocket I have is comprised of two stages: the first one has 3 engines, a center Swivel one (with 2 FL-T800s on top), and two radially mounted Reliant engines in an asparagus setting (so they have one FL-T800 on top each, with both of these fuel tanks feeding into the center one directly above the Swivel - this way, once the radial tanks are expended, they will be jettisoned with the Reliant engines).

The second stage is the orbital stage, having a single LV-909 Terrier with a FL-T400 on top (will talk about it later on).

The goal of this rocket is to carry scientific equipment to a space station at a 200km circular orbit over Kerbin, where it's currently being assembled for a mission to Minmus.

The problem I initially has is that the Delta-V calculation I done for the first stage gave me a result of ~1899m/s², which theoretically should not have been enough to allow me to leave Kerbin's atmosphere (as "Delta-V out" of Kerbin is 2500m/s²). Yet, I managed to dock with the intended station with about 60% of fuel remaining in the second stage (no cheats involved, I swear).

I've done all the calculations based on what's available at wiki.kerbalspaceprogram, making use of the "Advanced Rocket Design" and "Cheat Sheet" topics. Will go over the math now:

Starting up, I calculated the average Isp of the three engines at sea Level, which was pretty much: (F1+F2+F3/(F1/Isp1)+(F2/Isp2)+(F3/Isp3) being F=Thrust at sea level. This gave me an AvgIsp of 261 (which I called Isp1). Right after, I got the total mass of the craft (M0=28556t) and the first dry mass (aka: the mass with empty radial tanks before dropping them and the Reliants; which I called M1=20556).

I also calculated the new mass right after dropping the radial tanks and with full center tanks and swivel engine (M2=16646); and dry mass for empty center tanks (M3=8646).

Based on this, I calculated 2 delta-Vs for the first stage: Delta-V1, while both the Reliants and Swivel were firing; and Delta-V2, after the Reliants were dropped and only the Swivel was firing and taking fuel from it's own tanks now.

So, Delta-V1 = Isp1(261)*g[9,81]*ln(M0/M1)[0,32] obtaining a value of ~819m/s².

Did the same for Delta-V2, calculating the Isp2 for the Swivel only part of the flight, for which I got an Isp2 of ~167.9; then Delta-V2 of 1070m/s²

I then made the sum between both Delta-Vs, obtaining that nasty odd value of ~1889m/s².

As for the second stage, it gave me a Delta-V value of 276.6m/s², adding the whole sum to 2175m/s² (which shouldn't even be enough to take me out of Kerbin's atmosphere, let alone docking. The whole flight from Launch to a circular 200km orbit should require ~4844.88m/s², more than twice what I had!

Some thought and considerations (and questions):

1. I know the Delta-V I calculated is lower than the real Delta-V, since, for all the first stage engines, I only accounted for the Sea Level Isp and ignored the Vacuum Isp - while in reality the higher I went, the more Isp I'd have, thus increasing my Delta-V - although I don't believe it would have such an impact on the Delta-V.

2. I tried being efficient during the atmospheric flight, avoiding overspeed and unnecessary drag, which caused me to lower the throttle quite a bit (especially while the 3 engines were firing) and in turn increase the engine-on time, resulting in more Isp since I was ever higher with the engines on. This goes back to point 1, since I only considered Isp for Sea Level even though half of my fight happened at high altitude / low pressure / higher Isp environments. Could this also justify the Delta-V discrepancy?

3. Is there a way I can calculate Isp at an specific altitude so I can be more accurate (instead of only taking into account the Vacuum Isp for the 2nd/orbital stage and ASL Isp for the first stage)?

4. I tried repeating the math but assuming I'd not fire the Swivel until the Reliants were dropped. In the end it gave me a noticeably higher Isp and Delta-V, although still not as high as theoretically necessary. This is kinda odd though, shouldn't firing all engines together but feeding only from the radial tanks be more effective?

Thanks. Would love to hear what I've been doing wrong and hope I didn't give too much headache to people trying to read this. (And yes, I'm super jealous of you PC players with all the fancy Kerbal Engineer calculating stuff!)

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## Question

## Arch3rAc3

Hello!

Firstly, I know questions like this one have already been made both in and out of the forums before, yet every thread I found and read do not fix my problem or give me an idea of what I'm doing wrong. Also, sorry if this ends up a bit too long and technical, I want to try and make it as clear and detailed as possible, especially when explaining the math I did, so it doesn't confuse or give the reader a headache.

So... I finally decided to play KSP [more] seriously, disabling "revert flight" and trying to calculate the rocket performance and everything else before launch to minimize failures. I'm playing the Enhanced Version for the Xbox, which should be pretty much a 1.2 stock for PC.

The rocket I have is comprised of two stages: the first one has 3 engines, a center Swivel one (with 2 FL-T800s on top), and two radially mounted Reliant engines in an asparagus setting (so they have one FL-T800 on top each, with both of these fuel tanks feeding into the center one directly above the Swivel - this way, once the radial tanks are expended, they will be jettisoned with the Reliant engines).

The second stage is the orbital stage, having a single LV-909 Terrier with a FL-T400 on top (will talk about it later on).

The goal of this rocket is to carry scientific equipment to a space station at a 200km circular orbit over Kerbin, where it's currently being assembled for a mission to Minmus.

The problem I initially has is that the Delta-V calculation I done for the first stage gave me a result of ~1899m/s², which theoretically should not have been enough to allow me to leave Kerbin's atmosphere (as "Delta-V out" of Kerbin is 2500m/s²). Yet, I managed to dock with the intended station with about 60% of fuel remaining in the second stage (no cheats involved, I swear).

I've done all the calculations based on what's available at wiki.kerbalspaceprogram, making use of the "Advanced Rocket Design" and "Cheat Sheet" topics. Will go over the math now:

Starting up, I calculated the average Isp of the three engines at sea Level, which was pretty much: (F1+F2+F3/(F1/Isp1)+(F2/Isp2)+(F3/Isp3) being F=Thrust at sea level. This gave me an AvgIsp of 261 (which I called Isp1). Right after, I got the total mass of the craft (M0=28556t) and the first dry mass (aka: the mass with empty radial tanks before dropping them and the Reliants; which I called M1=20556).

I also calculated the new mass right after dropping the radial tanks and with full center tanks and swivel engine (M2=16646); and dry mass for empty center tanks (M3=8646).

Based on this, I calculated 2 delta-Vs for the first stage: Delta-V1, while both the Reliants and Swivel were firing; and Delta-V2, after the Reliants were dropped and only the Swivel was firing and taking fuel from it's own tanks now.

So, Delta-V1 = Isp1(261)*g[9,81]*ln(M0/M1)[0,32] obtaining a value of ~819m/s².

Did the same for Delta-V2, calculating the Isp2 for the Swivel only part of the flight, for which I got an Isp2 of ~167.9; then Delta-V2 of 1070m/s²

I then made the sum between both Delta-Vs, obtaining that nasty odd value of ~1889m/s².

As for the second stage, it gave me a Delta-V value of 276.6m/s², adding the whole sum to 2175m/s² (which shouldn't even be enough to take me out of Kerbin's atmosphere, let alone docking. The whole flight from Launch to a circular 200km orbit should require ~4844.88m/s², more than twice what I had!

Some thought and considerations (and questions):

1. I know the Delta-V I calculated is lower than the real Delta-V, since, for all the first stage engines, I only accounted for the Sea Level Isp and ignored the Vacuum Isp - while in reality the higher I went, the more Isp I'd have, thus increasing my Delta-V - although I don't believe it would have such an impact on the Delta-V.

2. I tried being efficient during the atmospheric flight, avoiding overspeed and unnecessary drag, which caused me to lower the throttle quite a bit (especially while the 3 engines were firing) and in turn increase the engine-on time, resulting in more Isp since I was ever higher with the engines on. This goes back to point 1, since I only considered Isp for Sea Level even though half of my fight happened at high altitude / low pressure / higher Isp environments. Could this also justify the Delta-V discrepancy?

3. Is there a way I can calculate Isp at an specific altitude so I can be more accurate (instead of only taking into account the Vacuum Isp for the 2nd/orbital stage and ASL Isp for the first stage)?

4. I tried repeating the math but assuming I'd not fire the Swivel until the Reliants were dropped. In the end it gave me a noticeably higher Isp and Delta-V, although still not as high as theoretically necessary. This is kinda odd though, shouldn't firing all engines together but feeding only from the radial tanks be more effective?

Thanks. Would love to hear what I've been doing wrong and hope I didn't give too much headache to people trying to read this. (And yes, I'm super jealous of you PC players with all the fancy Kerbal Engineer calculating stuff!)

Cheers.

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