Coriolis Drift of Discrete Objects

AI Thread Summary
The discussion focuses on developing a program to calculate Coriolis Drift for bullets, specifically addressing how to extend existing equations to include elevation changes in shooting scenarios. The initial equations provided calculate horizontal and vertical drift based on latitude, direction, and other parameters. The user seeks modifications to these equations to account for shooting uphill and downhill, aiming for a solution that remains simple enough for implementation in Pascal. The conversation also touches on the challenges of finding closed-form solutions and the potential to reframe the problem using Great Circle geometry to determine the latitude and direction of a second point on the sphere. The user is exploring ways to model these relationships mathematically while acknowledging the complexity involved.
Sooty
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I am writing a program aimed at 'gun nuts' designed to display Coriolis Drift of bullets (ie, 'discrete objects in free-fall', and not large fluid masses). Using the 2 equations below, I am able to calculate and display the values of Coriolis Drift (in terms of X & Y (vertical and horizontal)) as seen from a Horizontal Plane on the Earth's surface for all cases of Latitude and Direction, (the second 2 essential input terms).
These are my 2 equations:-

X:= T *Range * Sin(Lat) * Omega

Y:= Sin(Dir) * T * Range * Cos(Lat) * Omega;

Where:-
X = Horizontal Drift
Y = Vertical Drift
T = Time to Target
Range = Distance from gun to Target
Dir = Direction/Azimuth of fire in 'compass degrees' - 0 to 360
Lat = Latitude in degrees - from North (+90degrees) to South(-90degrees)
Omega = a Constant for Earth's Rotational Velocity

Now, I am attempting to extend my Coriolis Drift equations to address the same question for all values of Latitude and Direction beyond a Horizontal Plane (as above), to include Elevation above and below the Horizontal (ie, shooting uphill and downhill, +90deg/-90deg).

In short, what I am looking for is the necessary modifications/additions to the above equations (in a form that can easily be implemented in a Pascal program, hopefully using no more exotic math than basic Trig functions!) necessary to take the 7 terms above, plus:-

Elevation of fire from Vertically Up(+90degs) to Vertically Down(-90degs)

and return X and Y (Horizontal and Vertical relative to the Earth at the point in question) values for Drift, as seen by a viewer looking through a scope mounted on a rifle delivering the shot as described.

Thank you!
 
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I have always tracked trajectories by simulating the motion in very small steps. But those simulations had so much going on during the flight that it was completely different from a ballistic trajectory. I do not know if there are usable closed-form solution for your problem.
 
FactChecker said:
I have always tracked trajectories by simulating the motion in very small steps. But those simulations had so much going on during the flight that it was completely different from a ballistic trajectory. I do not know if there are usable closed-form solution for your problem.

'Very small steps'... yes, an 'iterative approach'... that is how I have done it in terms of getting figures for complete ballistic trajectories... literally 'finite element' calculations, a metre/meter at a time, and it gives excellent results. My current problem is really 'nit-picking on top of what is already close to being nit-picking'... so I may just have to accept that although there must be a solution possible, (hey, it's 'only geometry'!) I'm not going to find it!

Tnx for your input.
 
Reviewing my previous question, I believe I can 're-model' it in a way that is 'mathematically equivalent' and will so will allow me to continue with my project.
It addresses the question in terms of Great Circle/Spherical geometry, which although I can find relevant articles on the internet, they present their maths in ways that are waaay beyond my understanding.
So, instead of referring to anything about Coriolis, consider this:

So. Knowing point A on a sphere,
where the position of A is defined solely by Lat, where Lat = Latitude in degrees (as before)

And point B, whose distance from point A is defined (not by actual distance travelled) by the angle Asector, Where Asector = Angle of the sector of a Great Circle path that runs between them.

Now, the direction of point B relative to point A is Dir, where Dir = Direction/Azimuth in 'compass degrees' - 0 to 360 (as measured at point A) along the Great Circle path.

Questions:-
what is the value of Lat of point B?
what is the value of Dir at point A relative to point B on the great Circle path?
- - -
Hopefully, to clarify, if it's not already clear...
2 points on a Great Circle... Lat and Dir for each, obviously different... for my scenario, the distance between the 2 points is defined by the 'included angle' of the 'earth sector' covered, and not by the distance between them on the Earth's surface...
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