Thread: Thrust of Aircraft Engine vs Bullet?

I don't know why I thought of this question but I thought I'd ask to see if someone could help me answer it. My brain wanders a lot and I was actually thinking about noise reduction of an aircraft engine, but this popped out...

Suppose that a single 747 aircraft engine is bolted to some immovable object and operating at full power. Further suppose that a .44 magnum gun is placed at a distance d of 100 meters directly behind the rear exhaust of the engine and fired directly into the center of the rear exhaust. (see more info below)

Factoring only for the thrust and dimensions of the engine, the dimensions and weight of the bullet, and the initial velocity of the bullet, will the bullet reach and/or penetrate the rear exhaust, or will the thrust of the engine "blow" the bullet away before it can reach the exhaust?

Remember, we can take it that there is no gravity and that the bullet is fired in a straight line directly into the middle/center of the exhaust. Any arbitrary or complex factors such as wind (other than the thrust) or vortices within the cone of thrust coming out the back of the engine can also be negated. What I DO want to have included in the calculation is the dissipation of thrust forces as they come out the back of the engine i.e. the thrust force at 3m from the exhaust is not the same as the thrust force at 4m from the exhaust.

Now, I know that a lot depends on the bullet. I'm having trouble finding exact dimensions, but assume a solid point bullet with an initial velocity of 410m/s, a weight of 19g and bullet dimensions of base diameter 11.6mm, tip diameter 10.9mm and length 8mm.

For the engine, I am less certain. It looks like the GEnx-2B engine used on the 747-800 has a maximum thrust of 75,000 lbs. What I don't know about is the rear exhaust dimensions - I would say to calculate just using the assumption of a 1.5-2m diameter rear exhaust, but please feel free to make accuracy adjustments as you see fit.

If the bullet does reach or penetrate the rear exhaust of the engine based on the above info, then how would one calculate a value for d where the bullet exactly reaches the rear exhaust, but does not penetrate?

Sorry for the long and bizarre question, but I hope some of you find it interesting.

Originally Posted by DuckWurth

I don't know why I thought of this question but I thought I'd ask to see if someone could help me answer it. My brain wanders a lot and I was actually thinking about noise reduction of an aircraft engine, but this popped out...

Suppose that a single 747 aircraft engine is bolted to some immovable object and operating at full power. Further suppose that a .44 magnum gun is placed at a distance d of 100 meters directly behind the rear exhaust of the engine and fired directly into the center of the rear exhaust. (see more info below)

Factoring only for the thrust and dimensions of the engine, the dimensions and weight of the bullet, and the initial velocity of the bullet, will the bullet reach and/or penetrate the rear exhaust, or will the thrust of the engine "blow" the bullet away before it can reach the exhaust?

Remember, we can take it that there is no gravity and that the bullet is fired in a straight line directly into the middle/center of the exhaust. Any arbitrary or complex factors such as wind (other than the thrust) or vortices within the cone of thrust coming out the back of the engine can also be negated. What I DO want to have included in the calculation is the dissipation of thrust forces as they come out the back of the engine i.e. the thrust force at 3m from the exhaust is not the same as the thrust force at 4m from the exhaust.

Now, I know that a lot depends on the bullet. I'm having trouble finding exact dimensions, but assume a solid point bullet with an initial velocity of 410m/s, a weight of 19g and bullet dimensions of base diameter 11.6mm, tip diameter 10.9mm and length 8mm.

For the engine, I am less certain. It looks like the GEnx-2B engine used on the 747-800 has a maximum thrust of 75,000 lbs. What I don't know about is the rear exhaust dimensions - I would say to calculate just using the assumption of a 1.5-2m diameter rear exhaust, but please feel free to make accuracy adjustments as you see fit.

If the bullet does reach or penetrate the rear exhaust of the engine based on the above info, then how would one calculate a value for d where the bullet exactly reaches the rear exhaust, but does not penetrate?

Sorry for the long and bizarre question, but I hope some of you find it interesting.

The bullet will destroy the exhaust.

The gas velocity encountered by the bullet near the exhaust will be rather small compared to the velocity already encountered by the bullet (about 1400 fps) and the time involved for any enounter with the exhaust gas is also quite small and hence the momentum effect will be small as well.

Not sure if this is quite this simple...
The thing to remember is that a handgun projectile will usually travel at subsonic speeds (depending on the local speed of sound Sqrt(k*R*T) obviously). I believe the .44 Magnum (like all magnum calibers) is a bit of an exception since it will go up to about 1.4M. That said, exhaust gases can reach almost supersonic velocities at the exit (The one powerplant system I worked on got to about 0.95M at full thrust).
So how to calculate this? Well, I would propose that you look at the path and see if you can decelerate a bullet over 100m using a variable flow velocity. The varying amount of flow velocity is probably a bit tricky since it doesn't fall off based on any simple equation (that I know of). I would say that for a large engine like on a 747 the velocity drops to zero after maybe 500yds, but that is just a guess.
So the basic equation you would solve is this: on one side you have the kinetic energy of the bullet (1/2 m v^2) and on the other the work performed by the air friction. The work is simply force*distance where the force is CD*(1/2*rho*v^2*A) with a coefficient of drag somewhere around 0.9. Density will be fairly low (due to the higher temperatures, say around 1 kg/m^3).
The tricky part is getting the velocity v... both because it will be supersonic (so I'm not sure if the equation will even hold true) and because it will change both as a function of proximity to the engine as well as distance traveled.
Do you concur with this idea/approach?

Let's run this as a brief thought experiment for argument's sake. Not actually knowing the value (or better, the function) of v, we can assume that to be the only unknown and see if the values are "back of the envelope" kind-of-plausible.
If we use Ebullet=.5*0.019*410^2=1600J on one side, we can solve for the average (whatever that means here) velocity. In this case (making the assumption that the equation for F holds even at these speeds) F=0.9*0.5*1*v^2*(9.3E-5m^2) or a value for the work W=4.2E-3*v^2. So solving these two for v gives v=600 m/s... based on this I would conclude that it is indeed possible that the bullet does not actually reach the engine. The statement I would make would be along the lines of "it is possible that..." since not having better information (such as the function of how the velocity drops off).

Originally Posted by Solveer

Not sure if this is quite this simple...
The thing to remember is that a handgun projectile will usually travel at subsonic speeds (depending on the local speed of sound Sqrt(k*R*T) obviously). I believe the .44 Magnum (like all magnum calibers) is a bit of an exception since it will go up to about 1.4M. That said, exhaust gases can reach almost supersonic velocities at the exit (The one powerplant system I worked on got to about 0.95M at full thrust).
So how to calculate this? Well, I would propose that you look at the path and see if you can decelerate a bullet over 100m using a variable flow velocity. The varying amount of flow velocity is probably a bit tricky since it doesn't fall off based on any simple equation (that I know of). I would say that for a large engine like on a 747 the velocity drops to zero after maybe 500yds, but that is just a guess.
So the basic equation you would solve is this: on one side you have the kinetic energy of the bullet (1/2 m v^2) and on the other the work performed by the air friction. The work is simply force*distance where the force is CD*(1/2*rho*v^2*A) with a coefficient of drag somewhere around 0.9. Density will be fairly low (due to the higher temperatures, say around 1 kg/m^3).
The tricky part is getting the velocity v... both because it will be supersonic (so I'm not sure if the equation will even hold true) and because it will change both as a function of proximity to the engine as well as distance traveled.
Do you concur with this idea/approach?

Let's run this as a brief thought experiment for argument's sake. Not actually knowing the value (or better, the function) of v, we can assume that to be the only unknown and see if the values are "back of the envelope" kind-of-plausible.
If we use Ebullet=.5*0.019*410^2=1600J on one side, we can solve for the average (whatever that means here) velocity. In this case (making the assumption that the equation for F holds even at these speeds) F=0.9*0.5*1*v^2*(9.3E-5m^2) or a value for the work W=4.2E-3*v^2. So solving these two for v gives v=600 m/s... based on this I would conclude that it is indeed possible that the bullet does not actually reach the engine. The statement I would make would be along the lines of "it is possible that..." since not having better information (such as the function of how the velocity drops off).

Most handgun bullets travel at substantially over the speed of sound. Exceptions are relatively slow projectiles like a .45 ACP whichin the 700 -900 fps regime, depending on the particular load (target loads are slower). Even most .22 projectiles are supersonic ( except for deliberately subsonic target loads). The figure of 410 that you seem to be using (fps ?) is about that of a low-powered target air rifle. Real bullets are much faster.

Exhaust from an engine might be sonic at the exhaust throat. That will occur when the pressure ratio is above the critical level, which is only about 2 for most gasses -- at a pressure in round numbers of say 30 psi. But that condition lasts only briefly as the gasses expand (going supersonic but losing density quickly and then shocking down to subsonic speeds as they encounter ambient air). If this source is accurate the exhaust velocity we are talking about is only 200 mph or about 300 ft/s immediately behind the engine. That is not high compared to the bullet velocity and it does extend that far. http://www.airliners.net/aviation-fo...ad.main/36524/

The question is not when the flow velocity drops to zero, but rather when the exhaust either is at low density or the speed is small compared to the speed of the bullet. That would happen rather quickly.

The bullet will have no trouble at all in reaching the engine. Remember that we are only talking about a brief period when it encounters increased air resistance due to the exhaust gasses. There will not be nearly enough time to reduce the momentum of the bullet significantly, let alone to stop it. Just think about the solid matter that a bullet penetrates quite easily.

Think about it this way. A handgun bullet has a normal range on the order of a mile. So it travels say a 1/2 mile at fairly high velocity, starting out at something like 1100-1200 fps. High speed exhaust of a jet engine will exist for a relatively small distance compared to that. So the exhaust of the engine will be equivalent to only a few tens feet of drag over a typical bullet trajectory. It won't stop the bullet from entering the engine.

Very interesting, thanks for speaking to a methodology for trying to solve. I had to read through a few times to get a descent understanding. Certainly the approach makes sense to me.

For the coefficient of drag... I'm wondering how you got 0.9?

The first commenters submission did make me think that would be impossible based on the fact that the bullet would only be within path of the engine's airflow for ~0.25 seconds (based on the gun being 100m away and having an initial bullet velocity of 410m/s). It's hard to imagine a lot happening in such a short period of time. But, if the air force is enough, then I guess it's possible. Also, I did say about increasing the gun range up to the maximum required to make it stop - in this case I think 500 yards is a good estimate.

All-in-all, it sounds like this is one of those things that would require experimentation to know for sure... but whose going to spend $10mil to buy a 747 engine just to fire bullets at it

I'm not sure if I can agree with the Dr...
The 410 is m/s not f/s so it is supersonic. By quite a bit. It doesn't matter how long the bullet is exposed to the jet stream, but what the work is that needs to be performed in order to overcome the counter air flow.
The values you provide do not make sense. The exhaust air in the engine will be kept as close to unity mach as possible since that increases the efficiency without getting shocks and associated issues. This is by design and not choice. If you are talking turbo-fan that is. If you consider the turbo-jet exhaust, things are obviously different since they aim at having a flight speed in the supersonic range, so the exhaust will need to be supersonic. But since this is a 747, the flow will be subsonic (though barely).
Regarding range of this plume, I really don't know. The aircrafts I worked on, the plumes used to reach several hundred feet, extrapolating that, I would assume a long plume for the 747 at TO thrust (there's probably something on that on google).
Also, note that the density of the exhaust will decrease the closer you get to the engine due to an increase in temperature.

The point I'm trying to make is that for a very short period (over maybe a few meters only), the relative velocity of the bullet to the exhaust stream is VERY high. The supersonic shock waves will take a lot of energy out of the bullet.
Do I say it won't make it? Not at all. But I have my doubts it this is such a clear cut answer.
Now if you really need an answer (and I think you don't), you could solve this numerically using a transsonic CFD code with a moving mesh (or something else). Very computationally intensive, but cheaper than to shoot an engine (which would likely not break but only get dented at the mixer plane).

Last item: the CD for the bullet was assumed identical/close to that of a cylinder. I just couldn't be bothered to calculate it... but 0.9 should be about right. Now if you use a different bullet (say a 9mil) you would have less drag but the energy would also be substantially lower.

Originally Posted by Solveer

By quite a bit. It doesn't matter how long the bullet is exposed to the jet stream, but what the work is that needs to be performed in order to overcome the counter air flow.

If you look at the problem in terms of momentum then the time over which force is exerted is the quantity of interest.

If you look at the problem in terms of work then it is force over distance that is of interest.

You can do it either way, but in this case I think momentum is the more transparent approach.

410 m/s is supersonic and in keeping with about what I would expect for a relativel high velocity handgun projectile.

That should quite easily buck the flow from the engiine.

You're right... solving this is not essential - I just thought it was an interesting problem that somehow jumped into my mind. I will look into transsonic CFD code with a moving mesh, but I have to be honest and say that i have absolutely no idea what that is/means, but I'd like to figure it out and I have a few powerful computers that I can let attack the problem for a few days, if need be.

FYI - I came across this engine simulator that seems to indicate that the output velocity (V-exit) of the engine could easily be upwards of 2,000 fps at full thrust (you need to select "Engine Performance" for "Output" to see those values.)

Originally Posted by DuckWurth

You're right... solving this is not essential - I just thought it was an interesting problem that somehow jumped into my mind. I will look into transsonic CFD code with a moving mesh, but I have to be honest and say that i have absolutely no idea what that is/means, but I'd like to figure it out and I have a few powerful computers that I can let attack the problem for a few days, if need be.

FYI - I came across this engine simulator that seems to indicate that the output velocity (V-exit) of the engine could easily be upwards of 2,000 fps at full thrust (you need to select "Engine Performance" for "Output" to see those values.)

That speed may not be unreasonable. The gas velocity immediately at exit will be the local speed of sound in the gas at the temperature at exit, which is a function or the thermodynamics properties of the gas but basically goes like the square root of temperature over molecular weight. It will speed up a bit and cool down a lot and lose density as it expands. But the regime of high speed will die out quickly once the gasses are expanding in the atmosphere.

The real key here is the dynamic pressure of the gas, from the perspective of the bullet, as a function of distance from the exit plane, and not the velocity per se.

You can probably find the equations describing the gas dynamics with a search. Look for "choked flow" and nozzle design via isentropic expansion.

Just as something you can use to calibrate yourself, choked flow occurs when the ratio of the driving pressure to ambient pressure reaches a critical value. The critical value depends on the gas, and in particular on the ratio of specific heats. However, for most gasses the ratio is roughly 2. So if you release gas from a tire at about 20 psi, the air will be supersonic (about 1100 fps) at the outlet. You would not expect that to stop a bullet. The point being that exhaust velocity at the outlet is not the whole story by a long shot.

Quite frankly if the exhaust gas would stop a bullet, you would expect that the exhaust from a jet engine would also turn a heat-seeking missile, which is not nearly so fast or dense. Turning your exhaust towards an incoming missile is not a recommended strategy. And no, the argument that the missiles are continuing to thrust won't work since the missiles are typically at terminal speed by the time of engagement.

I forgot the link for the engine simulator in my last post: http://www.grc.nasa.gov/WWW/K-12/airplane/ngnsim.html

I have to be honest and say that I don't know which of the two posed arguments here makes more sense, however I like that solveer is providing formulas and numbers, and he/she seems to have a logic that makes more sense to me. But, again, I greatly appreciate all of the input for what is ultimately an abstract question. But there's nothing wrong with flexing the brain muscle!

On the point of the heat-seeking missile, please consider that in the original posed question/problem that the engine is stationary and not in-flight. If the engine were in-flight and traveling at 500 mph (223m/s), would that velocity/energy not need to be subtracted from the plume's energy when tackling the question of how it would effect the missile? Plus, I don't think that the fact that the missiles are at terminal velocity negates the fact that they are continuously thrusting. At terminal velocity the missile is no doubt gaining on the aircraft. The force of the engine would slow the missile, no doubt, but because it continues to thrust it can push through the plume (though I bet it has to compensate some).

Originally Posted by DuckWurth

require experimentation to know for sure... ultimately an abstract question

No way. My first thought was fish ladders. You only get one try.

I think the thought experiement has been somewhat exhausted at this point. I'm still not sure though if the answer has been found. I took another look at the post and the only place I see a large amount of uncertainty is the equation for drag of the bullet. Obviously the velocity profile is unknown but my experience tells me that a large engine like that of a 747 will have a very long exhaust plume. Not nearly the velocity at the exhaust, but possibly quite high velocity anyway at a distance of 100m (~100yds). Just take a look at how far back other airplanes stay when a 747 takes off!
But that said, I agree that it 'could' be.

Now one point I actually wanted to pick up on was the 'I'll just pick up a CFD code and run it' part...
Any good CFD code (I'm used to work with Ansys CFX and Star-CCM+) will cost you. A lot. On top of that, running these kinds of simulations is not a simple thing. If I were to charge a client for something like this, you'd be looking at a cost of about 10k, taking about 2 months. Computer power is another thing. This is not the kind of computation you run on a desktop computer but rather a compute cluster with maybe 64 CPU nodes and some 128GB of RAM (plus about 1TB of storage for the solution)... And the flow would be supersonic all the way (likely). Now if you REALLY are comitted to this and don't want to spend the $$, there is an alternative on how the student/non-professional can approach this: you can download OpenFOAM (free/open source) CFD software (Linux) and build the solution in a two step approach. First, you simulate the plume of the engine that you define. You will need some definition of the exhaust nozzle of the engine and an idea of the mass flow/velocity/temperature. You would then simulate this to find a v/x relationship taking into account ground effects and thermal/buoyancy.
Next, you would create a denser mesh that simulates the bullet's behavior. This would be very dense around the bullet and gradually drops of over distance. The mesh would probably only measure some 1m around the bullet (definitely a lot longer than wide/high) so as to capture the shock waves (small but important). You would then treat the bullet as fixed and provide a function of the flow past the bullet as a function of time (to mimic the bullet approaching the engine). This part would be required to account for the resultant drag since that will define the instantaneous velcity at the next time step.
Once you have that, bake it in a transient (time steppin) fashion over a very small time step (~1us)...
Does this sound easy? No, absolutely not. In fact, if someone came to me with this problem, I would recommend doing it a different way (like the one described above, maybe using a spreadsheet and doing a CFD simulation for the plume only).
Regarding the OpenFOAM software package, if you are the really curious type, I recommend you take a look at that, but don't expect anything simple. I've worked with CFD codes for some time and this is not at all the easy-to-learn kind. The easiest one I've ever come across is CFDesign, but the results/capabilities are not/were not up to par IMHO. Comsol is another one if you have the 15k handy...

But good to flex those brain muscles, I agree. I'd be curious for someone to put together a spreadsheet using the kinetic energy/work performed spreadsheet and creating a function of exhaust velocity vs. distance.

I just wanted to say thanks again for the great info and recommended approach... compute power should be available to me if I need it (I have access to one of the top 3 "cloud computing" providers).

I've downloaded OpenFOAM, which I'm about to compile. I'm sure there'll be enough here to keep my working for a few months in my leisure time... a nice new hobby I'll report back if I get anywhere with it.

Merry Christmas and Happy New Year.

A point of advice: if you use finite elements, you have to make sure to know how it works and what is happening. Finite element methods nearly always give a result, but it's not always the correct one. It is very easy to do something wrong without knowing it.
I don't mean to discourage, but don't jump in it too lightly, especially in CFD.

If you're looking for an open source FEM package: Elmer is free, but I haven't used it myself, and I have no idea how difficult it would be to implement this problem.

Originally Posted by Bender

A point of advice: if you use finite elements, you have to make sure to know how it works and what is happening. Finite element methods nearly always give a result, but it's not always the correct one. It is very easy to do something wrong without knowing it.
I don't mean to discourage, but don't jump in it too lightly, especially in CFD.

If you're looking for an open source FEM package: Elmer is free, but I haven't used it myself, and I have no idea how difficult it would be to implement this problem.

The CFD codes with whch I am familiar are finite difference codes, not finite element codes.

Agree with the previous posts... CFD is not something you kind of pick up on the side. If you are interested in numerical analysis, I recommend you start off slow with something along the lines of simple/linear FEA, structural or otherwise. That will get you a basic idea of what it is you are dealing with using simpler math than you will encounter in CFD. Before you hop onto the CFD bandwagon, also take a look at thermal finite differences method. CFD is IMHO probably the toughest numerical simulation that is used in industry though in many ways also the most rewarding. If you are just interested in "playing with it" as many people do, take a look at Blender from www.blender.org. Though that is an animation software package (and not overly easy to pick up... but then again you are considering learning OpenFOAM which is probably an order of magnitude harder), it has a built-in LBM flow solver that I have come to love (also the price: free).
You may also want to browse the web & wikipedia for some primers. Back in the day I coded my own differences code to do some fairly simple heat transfer stuff. Though the underlying equations seem quite simple (at least for the case of heat transfer and stress/strain), the numerical implementation can be very though, especially when you are dealing with 3D and not just 2D & 1D. Not to mention the meshing aspect that can be a job in itself.

Interesting link to Elmer, didn't know of that one. Will take a closer look. It is nice to see that there is an interface to GID. Though I'm not a huge fan of GID, its easier than to create the mesh at command level! Will definitely take a closer look at this one.