Delta V and the Oberth Effect

[ALaz1]

I have three questions:

1. What is Delta V? (A simple explanation)

2. Why is Delta V the same for big ships as well as small ones?

3. Why and how does the Oberth effect work?

Thanks

[IncongruousGoat]

1. Delta-V is a measurement of any given vessel's ability to change its velocity. We use it as a measurement of how "far" a vessel can travel since all that matters in orbital mechanics is your ability to preform burns, i.e. change your velocity.

2. The reason Delta-V can be the same for a large vessel and a small one is due to the way it's computed. Delta-V is given by the Rocket Equation :dV = I_sp*g*ln(m_w/m_d)

The figure we care about here is the m_w/m_d term. This (called the mass fraction) represents the ratio between your vessel's mass when it's full of fuel and its mass when empty. Given a certain engine efficiency, Delta-V scales with mass fraction, not with mass. Or, in other terms, the amount of Delta-V in your vessel depends on A: the efficiency of your engines and B: the fuel mass to not-fuel mass ratio, and not on the vessel mass itself.

3. The Oberth effect works because of the way work and energy are defined in physics.

First, in terms of work: Work is computed as F*d, or the product of force exerted time the distance it's exerted over. If you're moving faster, then you're going to travel further in a set amount of time. In the context of burn efficiency, it means that a given burn (force applied for a set time) is going to do more work if you're traveling faster, since the force will be applied over a longer distance.

Second, in terms of kinetic energy: Kinetic energy is computed as KE = 1/2 * m * v^2. This means that a linear increase in velocity will result in a quadratic increase in kinetic energy, with increases in velocity when already moving at high speeds producing large changes in kinetic energy compared to low speeds.

[Nibb31]

Delta v is the difference (=delta) in velocity (=v) between where you are and where you want to be. For example, you need a certain amount of dv to go from LEO to the Moon. And every spacecraft carries a certain amount of dv in the form of propellant. 

For vehicles of different sizes (or rather masses), the difference in velocity is the same, but the amount of energy to reach a specific velocity isn't. Orbital speed is a constant for each body, whether you're using Sputnik or Battlestar Galactica. However, the amount of energy needed to push Battlestar Galactica to orbital speed is going to be much higher, therefore Battlestar Galactica will need much more propellant, which will make it even heavier, and even harder to push around.

[ALaz1]

So there is a set amount of velocity needed to perform every type of maneuver, but bigger vessels might need more fuel to accelerate to that velocity?

[kurja]

Precisely. Just like how a big truck needs more oomph&fuel to go from naught to fourty than a small scooter, even though both accelerate just as much.

[sevenperforce]

12 hours ago, ALaz1 said:

1. What is Delta V? (A simple explanation)

We talk often about "orbital velocity", usually in reference to the velocity of a spacecraft orbiting in a circle just above the atmosphere (about 7.8 km/s or 17,000 mph), but there is a different velocity for every possible orbit. In order to move from orbit to orbit, you need to either increase or decrease your velocity, which requires you to fire your engines. The greek letter "delta" is used in physics and mathematics to refer to a change in some physical quantity, so "delta-velocity" or "delta-V" is used to represent the change in velocity (e.g., between two orbits).

But since we don't have infinite fuel, we can't just fire our engines whenever we want for as a long as we want. Just like in a car, you need to keep an eye on your fuel tank. But how far will a given amount of fuel get you? Fortunately, you can use an equation (the Tsiolkovsky ideal rocket equation, or rocket equation for short) to figure it out. Plug in the mass of your spaceship, the total amount of fuel, and the exhaust velocity (also called specific impulse) of your fuel, and the rocket equation will tell you that if you burned all your fuel, it would change your velocity by some specific amount. And remember, a change in velocity is also called...delta-V. So if your fuel tanks give you the ability to change your velocity by 1,000 m/s, then you can execute any maneuver that requires you to change your velocity by 1,000 m/s or less.

The nice thing about this is that you don't need any complex math to figure out how far you can get. If you need to add 50 m/s to your orbital velocity now, and 100 m/s to your orbital velocity later, then just make you have at least 150 m/s of total dV in your tanks. Just add it up. Note, however, that you can't subtract. If you need to add 50 m/s now and then subtract 100 m/s later, then you'll still need 150 m/s of total velocity change; your engines don't care whether you're speeding up or slowing down.

Because the delta-V value is so useful, it is used for other things as well. If you are taking off from the ground and going to space, then you will experience drag due to friction with the air. Rather than having to calculate the forces on your rocket and subtract them from your engine thrust for every point along your ascent, you can just determine that the total air resistance will rob you of about 750 m/s of delta-V. In other words, you burn 750 m/s of dV in fuel just fighting air resistance on the way up.

12 hours ago, ALaz1 said:

2. Why is Delta V the same for big ships as well as small ones?

Well, the change in velocity you need to move between two different orbits doesn't depend on the size of your ship at all; it's just based on orbital mechanics. The mass of a satellite or spacecraft doesn't affect its orbital velocity; and good thing too. That's how a small capsule is able to dock with a much larger space station: they both have the same orbital velocity and orbital location, even though their masses are different.

So a big ship needs the same change-in-velocity to move to a different orbit than a small ship does. However, the bigger ship will need more fuel. If the two ships have similar engines, it's fairly simple: both ships will burn approximately the same proportion of fuel to achieve the same change in velocity. For example, if the small ship masses 10 tonnes and needs to burn 2 tonnes of fuel to achieve a certain change-in-velocity, and the bigger ship masses 100 tonnes, then the bigger ship will need to burn 20 tonnes of fuel to achieve the same thing.

Note that if one ship has better fuel/engines (e.g., liquid kerosene on one ship and liquid hydrogen on the other ship), the ship with more energetic fuel won't have to burn as much of it for the same difference.

13 hours ago, ALaz1 said:

3. Why and how does the Oberth effect work?

We often think of gravity as a force, but gravity is actually a field which permeates and bends space. Just like a surfer can ride a wave in the ocean, a rocket's exhaust can "push against" a gravitational field in order to increase the change in velocity. The closer you are to a planet or other massive body, the more gravity there is, and the more of a push you can get. As a result, if you're in orbit around a planet, it's always better to make your biggest maneuvers as close to the planet as possible.

It gets better -- if you are coming from far away from a planet and passing very close to it, you can actually increase or decrease your velocity without burning your engines at all, just like a surfer can get a "kick" from the wake of a passing speedboat. However, this only works if you are passing by the planet; it doesn't work if you are already orbiting the planet.

It's as simple as that! 

[ALaz1]

Ok thanks a lot for the help. Now I can actually make it to other planets without guessing if I have enough fuel or not!

[sevenperforce]

36 minutes ago, ALaz1 said:

Ok thanks a lot for the help. Now I can actually make it to other planets without guessing if I have enough fuel or not!

Glad we could help!

Keep in mind that even though a higher orbit is slower than a lower orbit, you have to accelerate twice in order to reach it -- once in order to move into an oval-shaped transfer orbit, and second to circularize at the higher orbit.