Oberth effect - intuitive explanation(s)

[Frederf]

There is also no relation between Einstein's relativity theory and what is used as an example (Having to do something difficult and the time passes slow while it is pretty much faster when you are enjoying something) however examples from daily life makes it easier for people who are interested in science but they don't have the knowledge base for it. If we make it less scary for people than more people interested in science we get and more educated people we get in the future

And by the way, I didn't understand medicine ball example since I don't know the meaning for it even though I looked up the dictionary. May you explain that example a little more?

How is the exhaust "standing still" when the rocket is faster? Isn't the relative speed between the rocket and it's exhaust always the same? It might be standing still in relation to any other frame of reference, depening on the speed of the rocket and the energy released by the burn, but why does that matter?

I mean it's perfectly obvious that if energy is a function of mass times speed squared, inreasing the speed from 100 to 101 increases the energy way more than increasing it from 0 to 1. I just don't see how the bullet/cannon example makes this any easier to explain. Does this have something to do with relativity, perhaps? The exhaust also gets heavier as it gets faster, and flinging someting heavier gives you more energy.

Why it would matter is because it serves as a counter to the notion that KE is divided between the rocket and its expended propellant which would suggest that at some point you'd reach a maximum distribution in favor of the rocket at a finite speed. I was trying to dissuade this thought because it leads to incorrect conclusions.

The concept of 1000 to 1001 m/s being a bigger energy increase than 10 to 11 m/s is perfectly simple to follow but to many people it's unsatisfactory. They want to have an emotional understanding of their physical world which a mathematical explanation, however clear, doesn't provide. The search for the everyday example is to satisfy those people.

Relativity, as in Eisenstein relativity as opposed to the typical if-I-go-left-you-seem-to-go-right Galilean variety, isn't required at all. For the propellant to have relativistic mass it would have to have a relativistic exhaust velocity (aka relative to the rocket) not just a normal exhaust velocity happening at relativistic speeds as measured from elsewhere. Also one must remember that if the exhaust is relativistically heavy, so is the rocket. The two effects cancel.

You don't really need anything fancy to observe the Oberth Effect, as the Oberth Effect effectively states that it's easier to go faster when you're already moving fast. Even here on the ground, you can observe its effects quite frequently: consider how much longer it takes for a vehicle to go from a full stop to top speed than it does to go from halfway at top speed to top speed. Mind you, it's less obvious here on the surface of a planet since we have a number of factors (air resistance, surface friction, etc.) slowing us down. But it's still there nonetheless.

Not so much easier but more productive energetically. "Top speed" is a terrestrial phenomenon involving things like friction and drag. It takes a rocket longer to go from 0 to 2000 m/s than from 1000 to 2000 m/s too. A car has no greater ease going from 50 to 51 mph than it does from 10 to 11 ignoring the myriad of car-specific factors such as drag, friction, torque curves, gear ratios, etc. The quantity that is easier to tack on at higher speeds is energy. Assuming a vehicle can accelerate a given unit of speed it will provide more additional kinetic energy starting from a higher speed.

Dont complicate things. Wikipedia explains it very simple, its all in "useful" mechanical work. Read that paragraph. Here i quote:

"But when the rocket moves, its thrust acts through the distance it moves. Force acting through a distance is the definition of mechanical energy or work."

So by traveling faster, your thrust acts through more distance (in the same time) as it would when traveling slower.

Simple? Yes. Correct? Yes. Initiative explanation that everyone can relate to from everyday life? No. It comes back to one of those "see the equations work out!" arguments that fall flat with the layperson. "Wow, what a pitch! That fastball had 230 Joules on it!" Correct isn't always understandable. This is a really tough challenge because people do not see the world energetically. We think in force, distance, time, temperature but not linear energy. Our eyes see light bulb irradiance logarithmically! People are shocked at why car crashes at 50 mph aren't twice as violent than 25 mph.

I think pendula are a good avenue because they translate KE a measurement that we have little concept of linearly to height which we understand well. T = U = mg*h is a nice measuring stick. The trouble is finding a mechanism that adds a fixed deltaV so one can observe how its effect is different when applied at different speeds.

[AlternNocturn]

Anyone here played Metroid Prime? Remember the boost ball ability, how difficult it was to get the hang of the first time, but then eventually you realized that you needed to boost right at the bottom of the halfpipe to build up enough speed to get to the top? I think it's the same thing concerning the Oberth effect.

[miracmert]

Relativity, as in Eisenstein relativity as opposed to the typical if-I-go-left-you-seem-to-go-right Galilean variety, isn't required at all.

You got me wrong actually. I wasn't giving relativity as an example to Oberth Effect. I was just saying that Einstein described relativity to people in a way that has no relation with the real relativity but it made it easier for people to understand it. I was trying to say that the first example given for the Oberth Effect in this topic may not have any real connection with the Oberth Effect however it makes way easier for people to understand it and get more interested in science. I know that Einstein's relativity has nothing to do with this subject but thank you anyway for explaining

[Frederf]

I see. I'm reluctant to make analogies that aren't physical examples of what's being described. Telling someone "it's just like a fish pedaling a bicycle" when it's not is putting a stubborn roadblock in the road to future understanding no matter how convenient or feel-good it happens to be now. Understanding comes not from memorizing an outcome but seeing the process and being able to verify it. A memory device that cheats to give the right answer is only that, not understanding.

[Cronos988]

interesting discussion

I am actually not looking for an everyday example so much, rather I am trying to understand how the transfer of energy between rocket And propellant works.

If we assume the rocket is a barrel, and instead of a continous burn, a single projectile is ejected by an explosion, then the energy of the explosion is transferred to both barrel And projectile. But Intuition tells me that both would get the same energy everytime, equally split between them. Yet their relative masses and the speed of the entire system apparently matter. Looking at the explosion, I cannot tell why.

Edited July 21, 2013 by Cronos988

[Somerled]

Most explanations, intuitive or not, seem to miss the point of the Oberth effect. It's not mechanical force acting through a distance, since it's valid for impulsive forces (and is described as such, in fact). It's not the mechanical or chemical work of the propellant/rocket system, as it's valid for any system where a mass (of any proportion) is ejected from a system. And momentum is not affected: you'll always get the same delta-v from the same burn (notwithstanding any other physical effects) regardless of velocity or position within a gravity well.

It has to do entirely with how you define your reference frame. Oberth originally described it between two systems, one considered at rest and one considered in a frame moving with a velocity oriented with the direction of motion of the mass of interest (the rocket). Kinetic energy, and therefore a change in kinetic energy, relies on the reference frame you define it in, and only this change in energy for the rocket is larger in the moving reference frame. Oberth supports this by proving that energy is conserved, momentum is conserved, but the mass of interest receives more kinetic energy in the moving reference frame versus the stationary reference frame. And the choice of reference frame is arbitrary.

Want to see this in action? Get a rocket into orbit. Any orbit will do but to ease your mind, make it circular. Now, click on your speed readout above the nav-ball to change between surface and orbital speed readouts. Notice how it changes? Your velocity within an inertial frame (relative to the universe, you could say) never changed, your mass never changed, nothing in the simulation changed; but your speed does change between these two reference frames. Therefore you'll have a different kinetic energy in either of these two frames. Lower surface speed to zero and you'll still have orbital speed. Go one step further and do the math on your change in kinetic energy (0.5*m*v*v before and after the burn) for both frames and notice the difference. Bang! Proved Oberth in a game.

In short, energy itself is relative. The binding law for energy is only its conservation, which is also relative. It's a meaningless term on it's own (similar to pressure or electric potential). Energy gains meaning only within its frame of reference. As such, it's less of a physical quantity and more a means of relating how physical quantities change in relation to each other.

Quick quiz: according to Oberth, will your change in kinetic energy be larger if you burn retrograde instead of burning at rest? Answer: no, but your exhaust's will.

[Cheaterman]

Very intuitive, problem is that your example has nothing to do with the oberth effect.

I certainly expected some people not to understand

[Cheaterman]

Anyone here played Metroid Prime? Remember the boost ball ability, how difficult it was to get the hang of the first time, but then eventually you realized that you needed to boost right at the bottom of the halfpipe to build up enough speed to get to the top? I think it's the same thing concerning the Oberth effect.

That's pretty much the hammock example again! We could also take a skateboarder on a half pipe: it's more efficient -assuming his foot can be faster than the max speed he's moving at- to accelerate more at the lower point of the half pipe than pushing himself further in the air when he's at the top.