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Karol van Kermin

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Posts posted by Karol van Kermin

    How are my calculations wrong?

    in Science & Spaceflight

    Posted · Edited by Karol van Kermin

    9 minutes ago, Ultimate Steve said:

    If you're using KSP or RSS, keep in mind that gravity does not remain constant. 

    So in short: my formulas aren't useful if I do not take the change of gravity into account?

    Edit: Also, does gravity really change that significantly, so that I can miscalculate by about 500km?

    How are my calculations wrong?

    in Science & Spaceflight

    Posted

    Hey there fellow Kerbonauts!

    Recently I have been attempting to find an elegent formula with which I can calculate the apogee of a vertically flying rocket in a simplified system (no aerodynamic resistance and earth acceleration remains constant). I started off by defining the overall force F as the sum of all forces acting upon a vertically flying rocket. FT is the Force exerted by the engine and FG is the gravitational force pulling the rocket downwards (hence the negative sign):

    F = FT - FG
     

    Spoiler

     

    Since the mass of a rocket is changing over the time I described the mass at a given time t with the following formula, whereas M is the initial mass and m' is the fuel mass flow rate in kg/s:

    m(t) = M - m' * t

    Dividing the sum of all forces by the current mass gives us the acceleration of the rocket at the time t (FG/m(t) = g, because FG = m(t) * g).

    a(t) = F/m(t)

    a(t) = FT/(M - m' * t) - g

     

    Spoiler

     

    By integrating this formula in the interval [0;t] I get the following formula:

    v(t) = (FT/m') * ln[M/(M-m' * t)] - g * t

    FT/m' = ISP

    Intergrating the formula for the velocity at the time t should give us the track covered by the rocket after the time t:

    s(t) = ISP * {t * ln(M2 - M * m' * t) + (M/m') * ln[M/(M - m' * t)] - t} - g * t2/2

     

    Spoiler

     

    If I want to calculate the altitude at which the main engine cuts off (MECO), I first need to calculate the burn time:

    tMECO = (M - m0)/m' = mT/m'

    M ... total mass of the rocket

    m0 ... mass of the rocket without any fuel

    mT ... fuel mass

     

    Spoiler

     

    Having found the MECO time and thus the altitude and velocity at this given moment, I have to create a parabolic function using the following inputs:

    s(tMECO), v(tMECO), a = - g

    h(t) = - g * t2/2 + v(tMECO) * t + s(tMECO)

     

    To test my formula I built a small rocket and calculated that its Apogee should be at around 1017.391km. Because I was ignoring atmospheric drag in my formulas I assumed that the real apogee was going to be lower than the one I calculated. However, the opposite was true: In the demonstration my rocket reached an apogee of roughly 1500km. So I started thinking what could have caused such a miscalculation and I could not find an answer.

    I would love to hear your answers. Thank you very much for taking your time thinking about this issue and I apologize for my possible grammar and math mistakes.

    Fly safe! ;)

    Why can I achieve higher altitudes when flying in Orbit than straight up?

    in Science & Spaceflight

    Posted · Edited by Karol van Kermin

    17 hours ago, FleshJeb said:

    No, because you're changing the energy of the fuel you're blowing out the back by more as well.

    Although you've shown me the math behind this, I still cant wrap my head entirely around it.

    Since the thrust is in both cases the same, the delta V between the fuel and the spacecraft should be the same. How does a faster speed of the fuel and the spacecraft relative to the spectator have more energy, even though the delta V stays the same.

    I know that the math makes sense, but I just simply dont understand why it makes sense.

    EDIT 1:

    Also, after having thought about it, I came to the realization that you need more energy to accelerate an already moving object than a resting object, even in a perfect frictionless enviroment.

    Why can I achieve higher altitudes when flying in Orbit than straight up?

    in Science & Spaceflight

    Posted

    Hey guys!

    So today I was playing some KSP and I built a rocket which is meant to orbit Kerbin at a low altitude first and then increase the Apoapsis up to 1 000 000 km (So I can get some sweet science from low and high Orbit). After having achieved the 1 mil km I did a stupid mistake and I had to revert to start.This time, I decided to go for a more lazy approach. I decided not to achieve Orbit and just fly straight up. Now something happened which doesnt make any sense in my current understanding of the world. I was only able to achieve about 400 000 km - less than half the amount I was able to reach when flying in orbit.

    I dont know how this can make any sense: In my first flight I was spending way more time in atmosphere, why I should have lost more speed than in my second attempt. Also I just dont understand how flying vertically results in much lower altitudes than flying horizontally "only".

    I would be very happy if someone could explain the mathematics behind that. TY very much in advance!

    The Official Realism Overhaul Craft Repository.

    in KSP1 The Spacecraft Exchange

    Posted · Edited by Karol van Kermin

    28 minutes ago, Matuchkin said:

    I actually never understood why. I mean, sure, microgravity takes effect in such conditions, but isn't your rocket already accelerating? That should push the fuel backwards, which should fuel the engine, which should accelerate the rocket even more, which should push more fuel backwards, etc. How does that not happen?

    As much as I understand, you have to mind in which direction the fuel is accelerating relative to the engine. If the fuel is being accelerated by the same force as the engine is, then Delta a = ~0 (there may be some minimal difference, as the outter structure is being affected by aerodynamic resistance in the upper atmosphere). This means, that the fuel is not - minimally - changing its velocity to the engine.

    Interactive planets

    in KSP1 Suggestions & Development Discussion

    Posted

    Hey there!

    I haven't been playing ksp for a while now, but in the meanwhile, I came up with an, in my opinion, good idea! Currently Ksp offers you a bunch of planets, on which you can land on and visit different biomes, to get more science. And thats pretty much all you can do with planets... In my opinion kinda boring :/ .

    So my suggestion would be to make planets more interactive, and therefore much more interesting. As you may know, rocks are not solid. You can walk through them... But this is just one thing that bothers me. In my opinion planets also look a little bit boring. The textures are bad and surfaces can be either solid or fluid only. There isn't any kind of action on these planets. I mean, imagine big dusty storms on Duna! Or Geysirs on Jools moons! Just these little details would make the game so much more awesome!

    What do you think guys? I'd love to hear your opinion!

    Thank you very much!

     

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