Trajectory Input
Use SI units. Bearing is clockwise from true north.
Example Data Table
| Scenario | Latitude | Bearing | Speed | Elevation | Range | Interpretation |
|---|---|---|---|---|---|---|
| Northbound training case | 45° | 0° | 80 m/s | 35° | 500 m | Mostly east-west drift is expected. |
| Eastbound low arc | 30° | 90° | 120 m/s | 20° | 1,000 m | North and vertical terms become important. |
| Southern hemisphere test | -35° | 180° | 100 m/s | 40° | 900 m | Signs can reverse with latitude or bearing. |
Formula Used
The local Coriolis acceleration is calculated in east-north-up coordinates. The rotation vector is represented by north and upward components at the entered latitude.
The calculator integrates the acceleration over the active flight interval, t. The resulting first-order offsets are:
Here, φ is latitude, Ω is angular speed, g is gravity, and E, N, U indicate local east, north, and up axes. The model is accurate only as a small correction to an unperturbed ballistic path.
How to Use This Calculator
- Enter the launch latitude. Use negative values south of the equator.
- Set the bearing clockwise from true north. Avoid magnetic bearings unless corrected.
- Enter speed, elevation angle, launch height, and the desired horizontal range.
- Keep standard Earth gravity and angular speed for ordinary Earth calculations.
- Select Calculate Deflection. The result appears immediately above the form.
- Read signs carefully. Positive values identify east, north, up, right, or forward directions.
- Download the result as CSV or use the print control to save a PDF copy.
Understanding Rotational Ball Drift
A ball travels across Earth while the planet rotates beneath it. In a local frame, this rotation produces an apparent Coriolis acceleration. The effect is extremely small for ordinary throws. It becomes clearer when speed, flight time, and travel distance increase. Long-range projectiles, rockets, and atmospheric motion show the effect more strongly. This calculator estimates the drift for an ideal ballistic path.
On short paths, calculated motion can be microscopic. That does not make the model unimportant. It explains a rotating reference frame clearly. It also helps separate true forces from apparent forces seen by a ground observer. Results should always be interpreted alongside measurement uncertainty and experimental limits too.
Latitude and Direction
Latitude matters because Earth’s rotation axis has different local components around the globe. At the equator, the axis is horizontal relative to a local observer. Near either pole, it is nearly vertical. A northbound ball can therefore gain a different eastward offset than an eastbound ball. The launch bearing defines the horizontal direction. The elevation angle defines the vertical part of the initial velocity.
Integrated Motion
The calculation first builds east, north, and up velocity components. It then applies the local Earth rotation vector. The cross product of those vectors gives the Coriolis acceleration. That acceleration changes during flight because vertical velocity changes under gravity. Integrating it over the selected time gives approximate eastward, northward, and vertical offsets. The displayed total drift is the vector magnitude of those three components.
Flight Interval and Assumptions
The selected horizontal range determines the requested flight time. The calculator also checks the no-rotation ground-impact time. When the ball would land before reaching the entered range, the result stops at ground contact. This avoids presenting drift for a path that no longer exists. Launch height affects this impact check. Gravity may be adjusted for another planet or a controlled simulation.
Treat the result as a small-correction estimate. It assumes constant gravity, a spherical rotating Earth, and no air resistance. It ignores lift, wind, spin, terrain, latitude changes, and the tiny feedback caused by the drift itself. A real ball may move far more from wind than from Coriolis acceleration. The calculator is most useful for learning, preliminary comparisons, and carefully controlled long-range examples.
Reading the Output
Use consistent SI units. Enter metres, seconds, kilograms only where applicable, and degrees for angles. Bearing is measured clockwise from true north. A bearing of 90 degrees points east. Positive eastward, northward, and upward results describe the local displacement directions. The cross-range result is positive to the right of the launch direction. Negative values indicate the opposite direction.
Compare several cases rather than relying on one number. Try reversing the bearing. Try changing hemisphere or latitude. Try lowering the elevation while holding range constant. These tests reveal which velocity components drive the correction. Remember that Coriolis drift is not a substitute for complete exterior ballistics. Accurate targeting requires drag models, local winds, Earth curvature, and measured launch conditions.
Frequently Asked Questions
1. What does this calculator measure?
It estimates the small local displacement caused by Coriolis acceleration during an ideal ball trajectory. It reports east, north, up, along-track, cross-track, horizontal, and total offsets.
2. Why is latitude required?
Earth’s rotation vector has different local directions at different latitudes. Latitude changes the horizontal and vertical rotation components, so it changes both the direction and size of the estimated correction.
3. Which bearing convention is used?
Bearing is measured clockwise from true north. Zero degrees is north, 90 degrees is east, 180 degrees is south, and 270 degrees is west.
4. Does the tool include air resistance?
No. The model assumes an ideal projectile. Drag, wind, lift, ball spin, density changes, and terrain can dominate real-world motion and must be added separately for field predictions.
5. Why can the result stop before the entered range?
The calculator checks level-ground impact time. When the unperturbed ball lands before the requested range, it evaluates Coriolis drift only until that impact point.
6. What does a negative eastward result mean?
A negative eastward result means westward displacement. Likewise, negative northward means southward, negative upward means downward, and negative right cross-track means left of the launch bearing.
7. Is the vertical value a change in projectile height?
Yes, but only the first-order vertical correction caused by rotation. It is not the ordinary ballistic height, which is governed mainly by initial vertical speed and gravity.
8. Can I use another planet’s rotation rate?
Yes. Enter the planet’s angular speed and local gravity. The calculation remains an ideal local model, so atmospheric effects and non-spherical gravity are still excluded.
9. Is this suitable for sports throws?
It is useful for demonstration. For normal sports distances, the Coriolis effect is usually far smaller than release variation, wind, spin, and measurement uncertainty.
10. What does positive cross-track displacement mean?
Positive cross-track displacement points to the right when facing along the launch bearing. It is a convenient directional summary for comparing shots with different headings.
11. How should I use these results?
Use results as guidance, then validate with measured conditions.