๐งฎ Symbol & Equation Key
| Symbol | Meaning / Description | Units | Typical Value / Notes |
|---|---|---|---|
| m | Mass | kg / lbm | Trike, rider, or combined |
| W | Weight | N / lbf | W = m ร g |
| g | Gravity | 9.81 m sโปยฒ / 32.174 ft sโปยฒ | Standard g |
| v | Velocity | m sโปยน / ft sโปยน | |
| t | Time | s | Lap time |
| L | Lap length | ft / m | 3 485 ft |
| vavg | Average speed | ft sโปยน | L / t |
| KE | Kinetic energy | J / ft lbf | ยฝ m vยฒ |
| Wmech | Mechanical work | kJ | P ร t |
| ฮธtip | Tip-over angle | ยฐ | atan((bโ2)/h) |
| ay | Lateral accel. | ft sโปยฒ / g | g tan ฮธtip |
| R | Turn radius | ft | |
| vmax | Cornering speed | ft sโปยน / mph | โ(ay R) |
| C | Wheel circumference | in / ft | ฯ D |
| D | Wheel diameter | in | 20 in front |
| N | Cadence | rev minโปยน | v / 0 .357 |
| ฯ | Shear stress | psi | VโA |
| ฯb | Bending stress | psi | MโS |
| ฯvm | von Mises | psi | โ(ฯbยฒ + 3 ฯยฒ) |
| FoS | Factor of safety | โ | ฯy โ ฯvm |
๐ Key Performance Metrics
| Metric | Value | Units |
|---|---|---|
| Total Mass | 209.4 | lbm |
| Trike Weight | 39.4 | lbm |
| Rider Weight | 170 | lbm |
| Total Weight | 209.4 | lbf |
| Average Speed | 11.3 | mph |
| Top Speed (calc.) | 14.5 | mph |
| Lap Length | 3 485 | ft |
| Average Speed | 16.5 | ft sโปยน |
| Wheel Rev / Lap | 665 | rev |
| Tip-over Angle | 23 | ยฐ |
| Max Lateral Accel. | 0.42 | g |
| Max Safe Speed (R = 15 ft) | 9.8 | mph |
๐ Sample Calculations & Analysis
1. Mass, Weight & Velocity
Total weight: W = m ร g = 209.4 lbm ร 32.174 ft sโปยฒ = 209.4 lbf โ 932 N (95 kg).
Average lap speed: vavg = L โ t = 3 485 ft โ 211 s โ 16.5 ft sโปยน = 11.3 mph.
Wheel revs per lap (20 in front wheel): Nrot = L โ C โ 665 rev.
2. Energy & Power Budget
Kinetic energy @ 11.3 mph: KE โ 886 ft lbf โ 1.20 kJ.
Work per lap (84 W rider): Wmech = P t โ 17.7 kJ.
3. Stability & Cornering
ฮธtip = atan((19.5 inโ2) โ 23 in) โ 23ยฐ โ ay โ 0.42 g.
Max safe speed (R = 15 ft): vmax โ 9.8 mph.
4. Cadence vs Speed
v (mph) โ 0.357 ร Nrpm โ 11.3 mph โ 32 rpm, 14.5 mph โ 41 rpm.
5. Strength & Deflection Checks
- Axle (4140 HT): ฯ = 903 psi, ฯb = 39.7 ksi โ ฯvm โ 39.7 ksi, FoS โ 1.7.
- Seat-rail deflection: ฮด = 0.062 in < 0.25 in spec.
- Frame FEA: ฯvm,max = 2.795 ร 10โธ N mโปยฒ, ฯy = 6.204 ร 10โธ N mโปยฒ โ FoS โ 2.22.
๐ฉ Material & FEA Summary
Structural Material Comparison
| Component | Material | Yield Strength (psi) | Density (lb inโปยณ) | Machinability (%) | Weldability (%) | Source |
|---|---|---|---|---|---|---|
| Frame / Fork / Stem | 1018/1020 Steel | 53 700 | 0.284 | 60 | 85 | Salvaged |
| Rear Axle Tube | 4130 Steel | 97 000 | 0.283 | 35 | 60 | Machined |
| Rear Axle Stub | 4140 Steel (HT) | 69 500 | 0.284 | 40 | 40 | Machined |
| Bushings | 1018 Steel | 53 700 | 0.284 | 60 | 85 | Machined |
| Brass Spacers | C360 Brass | 49 000 | 0.307 | 80 | 20 | Machined |
FEA Setup & Critical Results
| FEA Case | Part | Load | Fixed BCs | Material | Max V.M. (psi) | Yield (psi) | FoS |
|---|---|---|---|---|---|---|---|
| Axle Shear / Bend | Rear Axle | 170 lbf@midpt | Bushings | 4140 Steel | 39 700 | 69 000 | โ 1.74 |
| Frame Compression | Down Tube | Rider | Headset + Axle | 1020 Steel | 16 200 | 51 000 | โ 3.15 |
| Seat Deflection | Seat Rail | 85 lbf end-load | Support base | 1018 Steel | 3 930 | 53 000 | โ 13.5 |
| Torsional Flex | Axle โ Frame | Turning torque | Axle ends | 4130 Steel | 21 900 | 97 000 | โ 4.43 |
Aggregate Strength & FoS
| Property | Value | Units |
|---|---|---|
| Rear Axle Shear Stress | 903 | psi |
| Rear Axle Bending Stress | 39 700 | psi |
| Yield Strength (4140 HT) | 69 000 | psi |
| Frame FoS (FEA) | 2.22 | โ |
๐ Download Full Calculation Package
A consolidated PDF (symbol tables, derivations, and appendix worksheets) is available for reference:
โฌ๏ธ Download Calculations PDF