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37 votes
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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
Organic Marble's user avatar
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 ...
Russell Borogove's user avatar
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 ...
SE - stop firing the good guys's user avatar
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 ...
Peter Nazarenko's user avatar
19 votes

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 ...
Antzi's user avatar
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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 ...
Russell Borogove's user avatar
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 ...
Russell Borogove's user avatar
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 ...
SE - stop firing the good guys's user avatar
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 ...
Loren Pechtel's user avatar
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 ...
Russell Borogove's user avatar
14 votes
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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 ...
Rainer P.'s user avatar
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14 votes

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 ...
Acccumulation's user avatar
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 $v$...
Litho's user avatar
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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 ...
Russell Borogove's user avatar
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 ...
Russell Borogove's user avatar
11 votes
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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. ...
Ruben's user avatar
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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 ...
BowlOfRed's user avatar
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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 ...
SE - stop firing the good guys's user avatar
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 ...
David Hammen's user avatar
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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 ...
A McKelvy's user avatar
  • 2,492
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 ...
Mark Adler's user avatar
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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 ...
IMil's user avatar
  • 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. $...
Litho's user avatar
  • 2,050
8 votes

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 ...
Rainer P.'s user avatar
  • 1,172
8 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....
asdfex's user avatar
  • 15.1k
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 ...
W H G's user avatar
  • 696
7 votes
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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 ...
CuteKItty_pleaseStopBArking's user avatar
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 ...
Russell Borogove's user avatar
6 votes
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From the General Thrust Equation towards Tsiolkovsky, how to explain dropping these terms along the way?

Check out the diagram at the top of the page that you got the equation from. Let's define our terms. $\dot{m}_e V_e$ is the momentum thrust term $\dot{m}_0 V_0$ is the incoming momentum term $(p_e - ...
Organic Marble's user avatar
6 votes
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Could asteroid 2012 XE$_1$$_3$$_3$ become a moon of Venus with the aid of rocket engines?

If it reaches Earth and Mercury, then it already sounds like the delta-V requirements for Venus capture are beyond hope. If it were to make close approaches to Venus, you might think of using Venus ...
SF.'s user avatar
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