Physics of Dropping Bombs from Stationary Aircraft

[jonbarril]

I am trying to understand the physics of dropping a bomb from an airplane for a bombsight simulator. In particular I'm trying to understand the effects of drag on the bomb in flight.

Let's say that a bomb, shaped like a blunt bullet, has lower drag in the forward direction than it does perpendicular to that direction. If I drop a bomb with a horizontal orientation (axis parallel to the horizon) from a stationary point and with no wind, as the bomb falls its fins will weather vane it, rotating it slowly into a downward orientation.

The question is, will the bomb fall straight down, or will differential drag as the bomb falls and slowly rotates from horizontal to vertical cause the bomb to drift in the direction that the bomb was originally facing, causing it to hit the ground with some lateral distance?

 

[Bystander]

It's laterally displaced.

 

[A.T.]

The question is, will the bomb fall straight down,

With air resistance the trajectory is not straight, regardless if the bomb rotates or keeps it's orientation.

 

[anorlunda]

Man, you are designing a bomb sight simulator and you don't know the answer to that question?

 

[jonbarril]

Bystander and anorlunda: The conventional wisdom is that drag is always in the opposite direction of the air flow. If the bomb falls straight down then how can there be a lateral force. My simulation of the bomb indicated otherwise and I started trying to figure out why. The math shows that it should be laterally displaced because of differential drag during the fall, but I wanted to confirm it to make sure I wasn't missing something.

AT: If the bomb shape were a sphere, with the same drag regardless of orientation, then the numbers and simulation indicate that the bomb falls straight down. If it is not and it maintains the same horizontal orientation throughout the fall then the drag vector would remain directly opposite the velocity vector. What would displace it laterally? Please explain. Did I miss something?

Thanks
--jon

 

[SteamKing]

Bystander and anorlunda: The conventional wisdom is that drag is always in the opposite direction of the air flow. If the bomb falls straight down then how can there be a lateral force. My simulation of the bomb indicated otherwise and I started trying to figure out why. The math shows that it should be laterally displaced because of differential drag during the fall, but I wanted to confirm it to make sure I wasn't missing something.

AT: If the bomb shape were a sphere, with the same drag regardless of orientation, then the numbers and simulation indicate that the bomb falls straight down. If it is not and it maintains the same horizontal orientation throughout the fall then the drag vector would remain directly opposite the velocity vector. What would displace it laterally? Please explain. Did I miss something?

Thanks
--jon

Planes don't drop bombs while remaining stationary; the plane usually has a forward speed while flying toward the target.

Regardless of whether drag on the bomb is accounted for, it will not drop straight down. While the bomb is accelerating vertically due to gravity, there is still a forward horizontal speed component due to the motion of the aircraft from which the bomb was dropped.

Bomb drops are special cases of general projectile motion, in that the bomb is released at the peak of a parabolic trajectory.

 

[Bystander]

Aerial bombs are usually dropped from moving aircraft. That said, lighter-than-air vehicles could conceivably be applied for "stationary" deliveries of ordnance. In such a case, assymmetric release results in lateral displacement in still air.

 

[SteamKing]

Aerial bombs are usually dropped from moving aircraft. That said, lighter-than-air vehicles could conceivably be applied for "stationary" deliveries of ordnance. In such a case, assymmetric release results in lateral displacement in still air.

OP specifically mentioned 'airplane'.

 

[anorlunda]

Have you studied WWII bomb sights, and their adustments and the data entered by the operator? Have you studied the history of bomb sight development?

 

[jonbarril]

Have you studied WWII bomb sights, and their adustments and the data entered by the operator? Have you studied the history of bomb sight development?

Yes. Thoroughly. But that has no bearing on the question I posed, which is one strictly having to do with the physics of the bomb flight through air, not the sight.

I specifically wanted to know what would happen if the bomb dropped from a *stationary* point so as to better and more fully understand the dynamics affecting the bomb. The subject of a bomb being dropped from a moving plane is extensively covered on the web and elsewhere, and is rather trivial. The subtleties of what happens as the bomb rotates and experiences differential drag during its flight, from a stationary point or otherwise, seems to be covered nowhere.

Keeping the airplane stationary simplifies the problem and I was hoping it would focus discussion on the differential drag aspect. So, back to the original question of what happens when the bomb is dropped, as described in my original post and in the subject line, from a stationary point. Does it experience lateral displacement, and is this due to the differential drag as the bomb rotates from a horizontal to a downward orientation?

 

[mfig]

Jonbarril,

Have you ever dropped a piece of paper originally held horizontally? If dropped from a good height it can end up laterally displaced by a substantial amount. Even a small, rigid piece of cardboard is moved laterally as it falls through still air. If you drop it perfectly, it almost looks like it slides on the air as it falls.

Thus I would say that there is always the potential for horizontal displacement any time a "flat" surface is at an angle from the vertical. The fins (and the side of the bomb itself, as it begins to rotate) are probably no exception, but the magnitude of the displacement would be much smaller due to the mass of the thing.

I would bet that if you are talking about dropping from thousands of feet the varied cross-breezes encountered on the way down would have a larger effect.

 

[jonbarril]

Yes, that seems intuitive and I thought of similar analogies. But then I started pondering and then researching the difference between lift and drag, and that's when things started getting really fuzzy. One interpretation is that drag is always opposite to the relative wind, and lift is due to a number of aerodynamic factors. One would not consider a bomb to have lift, and the direction the bomb falls, at least initially, is straight down, and hence the drag force is straight up. But then, depending on how you read the definitions, perhaps differential drag and the resultant lateral force could be considered as "lift".

Hopefully someone can confirm and perhaps even correctly label the forces at play during the bomb's flight from a stationary point. Besides being an answer to what has become a nagging question, it would also confirm that I am simulating the problem correctly.

Thanks
--jon

 

[DarioC]

I had to come back and do this over as I was still thinking of lateral as when dropped from an aircraft.

Try this: think of a bomb with fins, when dropped from a position as normal from an aircraft (horizontal), when dropped "straight" down from a fixed platform, as being a really poor glider. It has zero wings, but the topside of the bomb will still produce lift (and drag). So it will not fall straight down. As a matter of fact it will also be deflected in the opposite direction (likely several cycles) because it acts like a heavy short pendulum hanging from the fins. That is it will swing back and forth as it becomes vertically stabilized.

 

[A.T.]

AT: If the bomb shape were a sphere, with the same drag regardless of orientation, then the numbers and simulation indicate that the bomb falls straight down.

Yes, If the bomb is a non rotating sphere with center of mass at its center, and you drop from a stationary point on a windless day, it will just fall straight down (ignoring Coriolis effect etc.). But for anything that isn't so symmetrical, you cannot guarantee that all horizontal forces will cancel, so in general there will be some deviation (which might be negligible in practice).

 

[anorlunda]

Yes. Thoroughly. But that has no bearing on the question I posed, which is one strictly having to do with the physics of the bomb flight through air, not the sight.

You're wrong about them having bearing. The sights compensate for the physics of the bomb. If the designers of yore had to compensate for lateral displacement, is that not evidence that such displacement exists?

More interesting I think, is whether the WWII bomb sights had adjustments to compensate for the shape of the bomb. The Fat Man bomb was close to spherical, whereas other bombs were close to cylindrical. I don't know the answer to that. You studied them thoroughly, exactly what adjustments did they have?

 

[jonbarril]

It sounds like the consensus is that there is some manner of lift involved, regardless of the reason, and hence a lateral displacement. I am only accounting for "drag", not "lift", but apparently the effect is the same -- apparent lift (right?). And, this means that I am probably doing the bomb simulation correctly. Thanks.

Anorlunda: It is interesting to see how this problem was approached over 75 years ago. Nothing on the Norden sight compensates for specific bomb shape Everything about bomb characteristics was lumped into two numbers: "trail angle" and "fall time". What they had were extensive tables by bomb type, bombing altitude, and true air speed, and this provided trail angle and fall time which could be dialed into the bombsight. Evidently these tables were derived from actual drop tests at proving grounds and were considered classified just like the sight itself. The Sperry sight includes dials for bombing altitude and perhaps other factors, so less has to be in the tables, but I'm much less familiar with the Sperry sight -- a much more elegant sight that evolved into the modern autopilot (but which lost the bombsight "war" to the Norden).