๐ฏ Bungee Drop Calculator
Science Olympiad Division C - Cord Calibration & Drop Prediction Tool
Force-Length Data Entry
Calibration Instructions: Suspend your cord vertically and measure the stretched length at different force values. The first point must have a Force of 0 to define the unstretched length.
| Force (N) | Unstretched (cm) | Stretched (cm) | Strain (%) | Action |
|---|
Visualization
Pure Elastic Cord
\[ m(s^*) = \frac{1}{g(1 + s^*)} \int_{0}^{s^*} F(s) \, ds \]
\(L\) cancels โ peak strain \(s^*\) depends only on mass \(m\) (assuming \(\gamma = 1.0\))
Composite Cord (Inelastic + Elastic)
\[ m(s^*) = \frac{L_e}{g \, P} \int_{0}^{s^*} F(s) \, ds \]
\(L_e\) fixed, \(P = H - B - d\) โ peak strain \(s^*\) now depends on \(m\), \(L_e\), and \(P\)
Solve for \(s^*\), then \(\;L_i = P - L_e(1 + s^*)\)
Data Points
0
Max Force (N)
-
Max Extension (cm)
-
Drop Parameters
Calculator: Enter the drop height and mass to calculate the optimal cord attachment length. This uses your calibration data and energy conservation principles.
Regionals: 2.00-5.00m | States: 2.00-5.00m | Nationals: 5.00-8.00m
Light mass: 100-300g | Heavy mass: +200-300g
Safety margin to avoid touching
Calculation Details
Drop Simulation
Height & Forces vs Time
Record Trial Data
Trial Logging: Record actual drop results to refine your damping factor. The system will back-calculate the damping factor needed for each trial and recommend an optimal value.
Height of your bottle/device
The distance you aimed for
The damping factor assumed for this setup (you can edit this)
Closest distance the bottom of bottle got to ground
Total Trials
0
Fitted Decay Ratio (ฮณ)
-
Mean Residual (cm)
-
Std Dev (cm)
-
Trial History & Analysis
| Cord (cm) | Mass (g) | Height (m) | Target (cm) | Actual (cm) | Error (cm) | ฮณ Used | Trial ฮณ | Fitted Residual (cm) | Notes | Action |
|---|
Model Configuration
Export Model: Generate a complete lookup table and a fitted approximation function for your cord. This uses the calibration data and current damping factor.
Internal damping is linear in v (Fdamp โ v). Will use fitted value from Trials tab if available.
3D Visualization (Rotatable)
Click generate to see the 3D surface model.
Analytical: Strain vs Mass
Analytical: L vs Mass at h=1m
Generated Dataset (m, h, L)
| Mass (g) | Height (m) | Cord Length L (cm) |
|---|