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
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32
votes
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Why do some rockets not ignite all their engines during liftoff? (GSLV MK3 LV)
Besides limiting aerodynamic stress and drag losses as you and Antzi mention, using the core engine only at high altitude means the engine can be optimized for low-pressure use by putting a larger ...
- 167k
23
votes
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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 ...
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19
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Why do some rockets not ignite all their engines during liftoff? (GSLV MK3 LV)
Your assumption that we need max thrust at takeoff is partially wrong.
Although right at takeoff you do want max thrust, it might be counterproductive short after:
Your rocket and payload are Max G ...
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18
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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 ...
- 167k
17
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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 ...
- 167k
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
votes
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 ...
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15
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Is this a correct understanding of Tsiolkovsky's rocket equation?
Your question is about the behavior of the Tsiolkovsky rocket equation itself, in the limit of very small final mass (dry mass). Roughly: "is there any limit to delta-v in theory?"
Using MathJax:
$$
...
- 149k
15
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Is this a correct understanding of Tsiolkovsky's rocket equation?
The implication of the rocket equation is that linear increases in ∆v require exponential increases in mass ratio for a single stage.
There's not strictly a maximum delta-v -- if you redo your plot ...
- 167k
14
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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 ...
- 167k
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 ...
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13
votes
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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 ...
- 167k
13
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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$...
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12
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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 ...
- 167k
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 ...
- 6,667
10
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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
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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}$$
Accounting for variable mass is non-trivial, but as a ...
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10
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How do you find the propellant mass needed to reach an specified altitude? (altitude at end of burn plus altitude during coast)
How do you find the propellant mass needed to reach an inputted altitude?(altitude at end of burn plus altitude during coast)
The first thing you should be considering for any rocket mission is the ...
- 2,473
9
votes
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What is the relation between the rocket equation and work, energy and power?
If you're in vacuum, the power represented by the kinetic energy of the thrust is the thrust force times the exhaust velocity (g times Isp) over two:
$$P={g I_{sp}T\over 2}$$
One SSME in vacuum ...
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9
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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 ...
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9
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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. $...
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8
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Why do some rockets not ignite all their engines during liftoff? (GSLV MK3 LV)
Any excess energy, potential and kinetic, the boosters carry after separation is wasted. Therefore, you want to separate them at the lowest possible altitude and velocity, saving the core rocket's ...
- 1,172
8
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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 ...
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7
votes
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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 ...
- 167k
7
votes
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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....
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6
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Is this a correct understanding of Tsiolkovsky's rocket equation?
No, that is not quite right. Let's first state and describe the Tsiolkovsky Rocket Equation:
$\displaystyle \Delta v = V_e \times \ln(\frac{m_i}{m_f})$
$\Delta v$ is delta v, the change in velocity ...
- 4,566
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 ...
- 149k
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