37
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What does `ln` mean in the Delta V equation?
ln is a math function, the "natural log"
Most scientific calculators have a key for it.
See https://en.wikipedia.org/wiki/Natural_logarithm
- 189k
24
votes
Is g₀ a necessary term in Tsiolkovsky's Rocket Equation?
In the Tsiolkovsky rocketry equation, the $g_0$ can be confusing at first. The reason why it is there is because of the way ISP is calculated. The Isp can be calculate with the following equation:
$$...
- 6,836
23
votes
Accepted
How to account for burned fuel mass when calculating spacecraft acceleration?
The quantity you ultimately need when planning your manoeuvre is change in velocity, which in spaceflight terminology is called delta-v, $\Delta v$ (searching this term would give you a lot of ...
20
votes
Payload capacity of a rocket
The short answer is: Tsiolkovsky rocket equation. You need some velocity to achieve some position (an orbit or a body) in space. Farther a position - more velocity. More velocity - more propellant ...
- 1,183
18
votes
How much thrust needed to move 6,000 kg from LEO to Lunar Orbit?
What is needed is not thrust (above a certain basic amount), but delta-v, a function of the type of engine and the ratio between fueled mass and dry mass, according to the Tsiolkovsky equation.
The ...
- 172k
18
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Is g₀ a necessary term in Tsiolkovsky's Rocket Equation?
The US uses, and I'll be blunt, goofy units. The US definition of specific impulse explicitly uses $g_0$ to convert the effective exhaust velocity to units of time. Other places simply use the ...
- 77.4k
17
votes
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How much fuel is necessary to cause delta-v?
The Tsiolkovsky rocket equation tells you how much delta-V you get for a given exhaust velocity and full/empty mass ratio per stage. Typically you'll want to divide the total 9400m/s requirement into ...
- 172k
17
votes
Payload capacity of a rocket
It perhaps become clearer when stating what rockets do. They change velocity. In space terms, that's delta-v.
A rocket stage can only change your velocity some limited amount. Different targets in ...
16
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How much thrust needed to move 6,000 kg from LEO to Lunar Orbit?
While Russell Borogove mentioned it I think it deserves more focus: Thrust is the wrong thing to measure here. Thrust is how hard you can push--akin horsepower in your car. Your question is thus ...
- 11.7k
14
votes
Tsiolkovsky's Rocket Equation
$I_{sp}$ is inversely related to log of mass ratio if delta v is held constant, yes, but that's not how the rocket equation is usually applied.
The way the rocket equation is usually applied is that ...
- 172k
14
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Does a high staging number have diminishing returns? Is there a way to address that mathematically?
Any multi-stage rocket design has to obey three rules to achieve good performance:
Fuel type and engine design must allow for a high specific impulse. This is equally valid for single and multi ...
- 1,172
14
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What does `ln` mean in the Delta V equation?
It's the logarithmus naturalis. That wikipedia page was the first result when I googled "ln". If you encounter situations like this in the future and you're concerned that two letters aren't ...
- 695
13
votes
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Understanding Von Braun's Math: Theoretical Isp
I guess that it goes approximately like this: assume that the enthalpy change (I'll denote it $\Delta H$) is fully converted to the kinetic energy of the exhaust and the exhaust moves with velocity $v$...
- 2,120
13
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How does the Rocket Equation work when you use boosters?
For each phase of flight (stage or throttle variation or what have you) you weight the specific impulse (= exhaust velocity) by the propellant mass flow rates (i.e. consumption rates) of the different ...
- 172k
12
votes
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What is the distribution of ∆V amongst different stages of rocket flight?
Considering fuel consumption or energy expenditure may be misleading, because of the huge change in mass over the flight as fuel is expended. 2/3 of the fuel is expended by the first stage, which only ...
- 172k
11
votes
How cheap would rocket fuel have to be to make Mars colonization feasible (according to Musk)?
Frame challenge
This number has no basis in reality (other than possibly being a reverse calculation on the base of an available budget, see below). The quote is typical provocative Elon talk, just ...
- 2,489
10
votes
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What would the rocket equation look like for 4 ion thrusters?
The number of thrusters doesn't matter (that will change how quickly you can execute your $\Delta v$, not the ultimate amount of change you can perform). Just take the efficiency figure from the ...
- 7,129
10
votes
The thrust in the calculation of specific impulse
There's no "the" specific impulse, in the sense that the performance of a rocket engine varies over time. For a given moment in time, the instantaneous specific impulse can be derived from ...
10
votes
Comparing Newtons 2nd law and Tsiolkovskys
$$\sum F= ma + md/dt*v$$
This is erroneous, and everything after this is in turn erroneous. You should be using
$$\sum F= ma = m \frac{dv}{dt}$$
Accounting for variable mass is non-trivial, but as a ...
- 77.4k
10
votes
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How do you find the propellant mass needed to reach an specified altitude? (altitude at end of burn plus altitude during coast)
How do you find the propellant mass needed to reach an inputted altitude?(altitude at end of burn plus altitude during coast)
The first thing you should be considering for any rocket mission is the ...
- 2,657
9
votes
Accepted
What is the relation between the rocket equation and work, energy and power?
If you're in vacuum, the power represented by the kinetic energy of the thrust is the thrust force times the exhaust velocity (g times Isp) over two:
$$P={g I_{sp}T\over 2}$$
One SSME in vacuum ...
- 58.4k
9
votes
Accepted
Do lower pressure pressure-fed rockets get more Delta-V?
First of all: great observation! This is indeed the reason why pressure fed rocket engines are limited in possible chamber pressure, the added weight from the tanks isn't worth it at a certain point. ...
- 1,134
9
votes
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Payload capacity of a rocket
The other answers are correct, but might be too hard to grasp intuitively.
The simplest way to understand this is to reason the opposite way.
You have a rocket that can fly to the Moon. At some point ...
- 205
9
votes
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Where do the numbers 101,972 and 3,600 come from in terms of Thrust-Specific Fuel Consumption (TSFC or SFC)?
Specific impulse of $1~\text{s}$ is equivalent, in terms of speed, to $g_0\cdot 1~\text{s} = 9.80665~ \text{m/s}$, where $g_0 = 9.80665~ \text{m/s}^2$ is the standard gravitational acceleration. $...
- 2,120
8
votes
Comparing Newtons 2nd law and Tsiolkovskys
Isaac Newton stated that the forces equal the change in momentum:
$\Sigma F=\frac{d(mv)}{dt}$
When the rocket has a flow of $\dot{m}$ the result is
$\Sigma F=-\dot{m}v_e+m\frac{dv}{dt}$
where $v_e$is ...
- 806
7
votes
Accepted
Why is hydrogen better than helium as remass?
Why lighter atoms work better as fuel for a rocket:
The simple explanation, with concept only no numbers.
A rocket takes an amount of energy, puts that energy into matter, and that causes the matter ...
7
votes
Accepted
About optimal staging and structure fractions
First of all, I have to optimize an already-launched-rocket, which would mean that the rocket stages will already be optimized at maximum
Your assumption here is incorrect. Whenever optimization is ...
- 172k
7
votes
Accepted
Calculating the propellant needed for a trip from LEO to Low Mars Orbit at constant acceleration of 1g
TL;DR $\Delta v$ is only defined for one specific trajectory, but will be vastly different for different transfers.
$\Delta v = 6600 \rm{m/s}$ is only valid for a typical transfer like we do it today....
- 15.2k
6
votes
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"Oh-my-god" particle drive performance
Rocket equation starts with conservation of momentum:
$$\frac{dp}{dt} = m\frac{\partial v}{\partial t} + v\frac{\partial m}{\partial t}$$
But at such a high energy, the rest mass of the proton can ...
- 151k
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