Coriolis effect on ballistics and old chart

[davidwinth]

Hello,

I was looking through an old Naval gunnery guide that tabulates deflections due to the Coriolis effect. I must be reading this wrong or I don't understand how they are reckoning direction. If I am at the equator and I shoot north, shouldn't the bullet deflect the the right of the target? This table seems to indicate that the bullet will deflect to the left.

What is going on?

Thanks.

 

[Orodruin]

Is it possible they are tabulating how the aim should be deflected?

 

[anorlunda]

I don't understand how they are reckoning direction.

Huh? "True target bearing" is the direction.

 

[Vanadium 50]

A. Could it be a Southern Hemisphere table?

B. More generally, it would help to post the instructions for using that table, if you have them.

 

[Orodruin]

Could it be a Southern Hemisphere table?

"For north latitude use bearing at top of table. For south latitude use bearing at bottom of table."

B. More generally, it would help to post the instructions for using that table, if you have them.

Agreed. However, I still suspect this is how the aim should be deflected relative to the true target.

 

[DrStupid]

If I am at the equator and I shoot north, shouldn't the bullet deflect the the right of the target?

Would't that depend on the elevation? A horizontal shot should be deflected to East. A vertical shot would be deflected to West. I have no idea which effect dominates for real shots.

 

[jbriggs444]

Would't that depend on the elevation? A horizontal shot should be deflected to East. A vertical shot would be deflected to West. I have no idea which effect dominates for real shots.

At non-trivial ranges, naval gunfire generally involves a target which is at approximately the same elevation as the firing platform. An 8 inch 55 mount is not well suited for anti-aircraft work.

 

[DrStupid]

At non-trivial ranges, naval gunfire generally involves a target which is at approximately the same elevation as the firing platform.

I am talking about the angle of the barrel.

 

[jbriggs444]

I am talking about the angle of the barrel.

I stand corrected.

The vertical arc of the shot explains the consistently westward deviations seen in the chart for 0 degrees latitude. That westward bias due to the vertical arc is still present at other latitudes but is swamped by Coriolis due to the horizontal velocity.

I believe that you have answered the question in the OP.

 

[davidwinth]

Would't that depend on the elevation? A horizontal shot should be deflected to East. A vertical shot would be deflected to West. I have no idea which effect dominates for real shots.

Yes, so I think that may be the key. There is also a correction chart for the change in range due to the rotation of the Earth in that same gun's guide. Tell me if I am thinking about this correctly now. Since the chart is made for a specific gun and a specific initial velocity, the chart has to include things such as how high you would elevate the barrel of that particular gun to hit a target at the tabulated range, time of flight, projectile aerodynamic properties, and whatever else there is. So the tabulated values are really the net effect of those things taken together not specifically only the Coriolis effect. Is that correct now? That make sense since this is a gunners book to be used in the field quickly.

Also, here is a link to the other corrections if other people are interested.

http://www.eugeneleeslover.com/USNAVY/FC-APPENDIX-B-8IN-55.html

 

[Drakkith]

Tell me if I am thinking about this correctly now. Since the chart is made for a specific gun and a specific initial velocity, the chart has to include things such as how high you would elevate the barrel of that particular gun to hit a target at the tabulated range, time of flight, projectile aerodynamic properties, and whatever else there is. So the tabulated values are really the net effect of those things taken together not specifically only the Coriolis effect. Is that correct now?

The values are derived from all of those things, yes.

One question I have is why are the values negative only for the 0 and 10 degree tables? The difference in eastward horizontal velocity between the gun and the target because of the Coriolis effect makes it so that you would have to deflect the gun westward (negative values on the chart) to correct for this when the target is at another latitude. That effect appears to only increase as latitude increases. What other effect am I missing here?

 

[jbriggs444]

One question I have is why are the values negative only for the 0 and 10 degree tables?

@DrStupid has identified the relevant effect. At the equator, Coriolis is negligible for a projectile on a horizontal path regardless of its direction. However, Coriolis is not negligible for a projectile fired vertically. Such a projectile will be deflected westward. The higher the shooting angle (and the more powerful the propellant charge)(*), the higher the shot and the greater the westward deflection. This is reflected in the chart for 0 degrees. All of those listed corrections reflect a purely westward drift. The chart does not have a column for "short" or "long", so shots at 90 degrees (east) or 270 degrees (west) are listed with no correction.

A 0 degree (north) shot is deflected west (left).
A 180 degree (south) shot is deflected west (right).

At higher latitudes, the westward bias due to vertical Coriolis is still present, but it is swamped by the horizontal component. Shots at 0 degrees (north) tend to deflect rightward (east) due to the horizontal component and leftward (west) due to the vertical component. Shots at 180 degrees (south) tend to deflect west/right due to both components.

(*) Edit: A quick Google search indicates that 8"/55 has a 2500 fps muzzle velocity on a full propellant charge. The chart presented in this thread does not contemplate the use of a reduced charge for short ranges.

 

[Drakkith]

However, Coriolis is not negligible for a projectile fired vertically. Such a projectile will be deflected westward.

Okay. I had to look up more information on the Coriolis force, as I had no idea that a vertically fired projectile would drift west. I think things are starting to make sense now.

 

[FactChecker]

This is much more complicated than it appears at first. It would depend on the elevation shooting angle of the gun, the velocities of the shell while ascending versus descending, and the usual Coriolis of level flight. It's a difficult combination to figure out and the answers in the table show a resulting complicated pattern.
I suspect that the table results were first obtained experimentally rather than analytically.

 

[Orodruin]

I suspect that the table results were first obtained experimentally rather than analytically.

I suspect that results today are not obtained analytically either, but using computer simulation.

 

[sophiecentaur]

I suspect that the table results were first obtained experimentally rather than analytically.

Probably done analytically at first and then verified experimentally (with a bit of feedback by tiffling of the coefficients, no doubt).

 

[Vanadium 50]

I suspect that results today are not obtained analytically either, but using computer simulation.

The trend has been to go to guided munitions where this is not relevant. Modern guns have a "fire controller" instead of tables. I honestly don't know if they use lookup tables or analytic functions nor what difference that makes. It's essentially "I want the shell to hit over here" and "then these are your gun settings".

 

[FactChecker]

The trend has been to go to guided munitions where this is not relevant.

I would rephrase that to say that they are adjusted for, rather than irrelevant. That's along with other forces like winds, gravity, etc. But smart munitions are not universally used. There are still a lot of dumb ballistic munitions in the world.