Mechanics & power engineering

1. Roof pitch & gradient converter
2. RMS vibration & natural frequency
3. Single & three-phase motor calculator
4. Fuel heating value & energy density
5. Wind turbine power & Betz limit
6. Drag racing ¼‑mile predictor
7. Horsepower / torque / RPM solver
8. Suspension toe-out & rake angle

$$\theta=\arctan\!\left(\frac{\text{Rise}}{\text{Run}}\right),\qquad \text{Grade \%}=\tan\theta\times100$$

Pitch ratio expressed as Rise : 12 (e.g. 4:12). Source: 1728 Software Systems.

$$f_n=\frac{1}{2\pi}\sqrt{\frac{k}{m}},\qquad a_{\text{peak}}=\omega^2x_{\text{peak}}=(2\pi f)^2x_{\text{peak}}$$

Peak/RMS conversion: $x_{\text{rms}}=x_{\text{peak}}/\sqrt{2}$. $v_{\text{peak}}=\omega x_{\text{peak}}$. Source: Engineering ToolBox.

$$I_{1\phi}=\frac{P\cdot1000}{V\cdot\text{PF}\cdot\eta},\qquad I_{3\phi}=\frac{P\cdot1000}{\sqrt{3}\,V\cdot\text{PF}\cdot\eta}$$

$P$ in kW or HP (1 HP = 0.746 kW). Source: Engineering ToolBox.

$$\text{LHV}=\text{HHV}-2260\times(9\times H_{\text{mass}})$$

Approximate LHV accounting for latent heat of water vapour. Source: Engineering ToolBox.

$$P_{\text{wind}}=\frac{1}{2}\rho A v^3,\qquad P_{\text{turbine}}=C_p\cdot\eta_m\cdot P_{\text{wind}}$$

Betz limit: $C_{p,\max}=0.593$. $A=\pi R^2$. Source: Engineering ToolBox.

$$\text{ET}=5.825\!\left(\frac{W}{\text{HP}}\right)^{1/3},\qquad \text{MPH}=234\!\left(\frac{\text{HP}}{W}\right)^{1/3}$$

Empirical estimate for ¼-mile performance. $W$ in lbs, HP at flywheel. Source: 1728 Software Systems.

$$P_{\text{HP}}=\frac{T_{\text{ft-lb}}\cdot N_{\text{RPM}}}{5252},\qquad P_{\text{kW}}=T_{\text{N·m}}\cdot\frac{2\pi N}{60000}$$

Enter any two parameters; the third is solved. HP & torque curves cross at 5252 RPM. Source: 1728 Software Systems.

$$\theta_{\text{toe}}=\arcsin\!\left(\frac{\Delta d}{D_{\text{wheel}}}\right),\qquad \theta_{\text{rake}}=\arctan\!\left(\frac{h_{\text{rear}}-h_{\text{front}}}{L_{\text{wheelbase}}}\right)$$

Toe: linear difference across wheel diameter. Rake: chassis height differential along wheelbase. Source: 1728 Software Systems.