Long Jump Inputs
Enter the athlete’s takeoff speed, angle, heights, and gravity. The calculator treats the jump as a projectile motion problem and returns the predicted flight time and horizontal distance.
Calculated Attempts
Each calculation is stored below. Use the export buttons to download the dataset as a CSV file or a formatted PDF.
| Attempt | Speed | Angle (°) | Takeoff height (m) | Landing height (m) | Gravity (m/s²) | Flight time (s) | Distance (m) | Distance (ft) |
|---|
Example Data Table
This example table illustrates typical values for long jump attempts using different takeoff speeds and angles. Your calculated results appear in the table above.
| Scenario | Speed (m/s) | Angle (°) | Takeoff height (m) | Landing height (m) | Gravity (m/s²) | Predicted distance (m) |
|---|---|---|---|---|---|---|
| Training jump | 8.5 | 20 | 0.50 | 0.40 | 9.81 | 6.9 |
| Competition jump | 9.3 | 21 | 0.55 | 0.40 | 9.81 | 8.0 |
| High-altitude meet | 9.0 | 19 | 0.52 | 0.40 | 9.78 | 7.7 |
Formula Used
The long jump is modeled as a projectile launched with initial speed v at an angle θ from a takeoff height h0 to a landing height hL under constant gravitational acceleration g.
- Horizontal component: vx = v · cos(θ)
- Vertical component: vy = v · sin(θ)
-
Vertical motion equation:
h(t) = h0 + v_y · t − 0.5 · g · t² -
Time of flight is found by solving:
h0 + v_y · t − 0.5 · g · t² = hL -
This gives:
t = (v_y + √(v_y² − 2 · g · (hL − h0))) / g(taking the physically meaningful positive root). -
Horizontal distance (range):
Range = v_x · t -
Distance in feet is obtained using
1 m ≈ 3.28084 ft.
How to Use This Calculator
- Measure or estimate the athlete’s takeoff speed along the runway. Choose whether it is entered in meters per second or kilometers per hour.
- Enter the takeoff angle in degrees. This is the angle between the takeoff direction and the horizontal runway.
- Specify the center-of-mass height at takeoff and landing. If you are unsure, keep the default values or set both equal.
- Keep the default gravitational acceleration, or adjust it slightly for different locations or experimental scenarios.
- Click “Calculate Jump Distance”. The predicted flight time, distance in meters, and distance in feet appear in the results box.
- Every calculation is added to the attempts table. Use the CSV button to export data into spreadsheets, or the PDF button for a printable report.
- Compare multiple attempts with different angles or speeds to explore how technical changes influence overall long jump performance.
Long Jump Distance Performance Overview
Competitive long jump performance depends on controllable mechanical variables. This section explains how approach speed, angle, posture, and environmental conditions interact to determine realistic distances for training and competition analysis.
1. Approach Speed and Runway Rhythm
The athlete must accelerate smoothly along the runway, usually over eighteen to twenty six strides. Consistent rhythm helps maintain relaxation, allowing horizontal velocity to peak just before the final three controllable strides.
2. Takeoff Angle and Board Contact
Elite jumpers rarely use textbook forty five degree angles. Practical angles between eighteen and twenty four degrees balance horizontal speed preservation with enough vertical lift to produce optimal flight time without excessive braking at the board.
3. Center-of-Mass Heights
The calculator uses separate takeoff and landing heights to mimic real technique. A slightly higher takeoff center of mass compared with landing reflects erect posture at takeoff and crouched, heel-first landing positions inside the sandpit.
4. Flight Time and Body Positions
During the aerial phase, hang, sail, or hitch kick techniques adjust body shape without changing the parabolic path. The model therefore focuses on launch parameters, leaving technique expression to coaching analysis rather than altering trajectory physics.
5. Environmental and Gravity Effects
Small changes in gravitational acceleration, altitude, or runway surface stiffness can influence measured performance. Adjusting gravity allows simulations of jumps at sea level facilities compared with higher altitude locations or controlled biomechanical laboratory environments.
6. Fouls, Board Accuracy, and Safety Margins
In practice, athletes do not always hit the takeoff board perfectly. Coaches estimate safe target distances behind the board to avoid fouls. The calculator assumes a clean takeoff, so users may subtract planned safety margins.
7. Using Data to Guide Training
By saving repeated calculation attempts, practitioners can explore how realistic improvements in approach speed or angle change expected distance. Linking modeled values with video, timing gates, and split measurements supports evidence based technique refinement for each athlete.
Frequently Asked Questions
1. When should I use this long jump calculator?
You can use the calculator whenever you have runway speed, takeoff angle, and height estimates. It is useful for planning training sessions, testing technique changes, or checking whether competition goals look mechanically realistic.
2. Can I enter takeoff speed in kilometers per hour?
Yes. When you select kilometers per hour, the script converts values automatically into meters per second. This keeps all internal equations consistent while letting coaches enter data using their preferred timing systems.
3. Why do I sometimes see “no physical solution” errors?
If the error message reports no physical solution, the height, speed, or angle combination is unrealistic. Reduce extreme height differences, use smaller angles, or confirm that the takeoff speed falls within typical athletic ranges.
4. Does the calculator include wind assistance or resistance?
In practice, wind can significantly change measured distance. The current model does not directly include wind. However, you can compare calm and windy attempts by entering different effective approach speeds from timing gates.
5. Can I analyze the exported CSV in performance software?
Yes. The CSV export is designed for easy import into spreadsheets or athlete monitoring platforms. Once imported, you can graph relationships between speed, angle, and distance across training cycles or competition seasons.
6. How should I use the PDF report during coaching sessions?
The PDF export summarizes every stored attempt, making it convenient during field sessions. Coaches can print copies for debrief meetings, share digital reports, or archive performance snapshots for future comparison and season reviews.