Torque, power, energy*

Summary: Essential concepts for sizing a system ≤ 60 V: voltage, current, power, energy, torque; useful conversions; quick method and field example.

Learning objectives

Understand U (voltage), I (current), P (power) and E (energy) in a 48 V DC context.
Link electrical power (U × I) and mechanical power (n × C or τ × ω).
Quickly estimate a torque/power requirement and battery autonomy.

Key concepts

Voltage U [V]: electrical 'pressure'.
In mobility or tools: often 48 V DC for power; 5/12/24 V for logic/control.
Current I [A]: 'flow'.
Main source of heating (Joule losses ∝ I²R).
At a given power, increasing U allows reducing I and the cable cross-section.
Power P [W]: energy flow.
- Électrique : \(Pel=U×I\)

\(P_{el} = \text{Puissance électrique} (W)\)

\(U = Tension (V)\)

\(I = Intensité (A)\)

- Mécanique (rotation) : \(Pmec=τ×ω\)

\(Pmec = puissance mécanique (W)\)

\(τ = couple (N·m) — parfois noté C\)

\(ω = vitesse angulaire (rad/s)\)

Ainsi on peut aussi écrire : \(Pmec=C×ω\)

Energy E [Wh]: autonomy.
L’énergie représente une quantité totale que l’on peut consommer dans le temps.

\(E=P×t\)

Pour une batterie, l’énergie disponible se calcule à partir de la tension et de la capacité :

\(Wh=V×Ah\)

DC vs AC (very brief reminder)

DC (direct current): nearly constant voltage; comes from batteries (or AC/DC converters).
AC (single/three-phase): alternating voltage; distributed by the grid and available at power outlets (single-phase or three-phase).

Electric motor (rotating machine)

Reversibility: motor or generator depending on the direction of energy exchange (electrical/mechanical).
Useful quantities: rotational speed n [rpm], torque C [N·m].

Conversion de vitesse : \(ω=2π× \frac{n}{60}\)

où ω est la vitesse angulaire en rad/s

Force de traction à la roue : \(F_{traction}=\frac{r_{roue}}{C_{jante}}\)

où \(C_{jante}\) est le couple appliqué à la jante et \(r_{roue}\) est le rayon de la roue.

Puissance d'un moteur

La puissance mécanique instantanée vaut :

\(P_{mec}=C×ω\)

ou encore, en fonction de la vitesse en tr/min :

\(P_{mec}=C×(2π \frac{n}{60})

Batteries (useful reminders)

Capacity Ah → energy Wh via voltage:
\(Wh=V×Ah\)
(e.g.: 48 V × 200 Ah = 9600 Wh = 9.6 kWh)
Instantaneous power demanded from the pack:
\(P≈U×I\)
(Il faut vérifier que le courant I reste inférieur aux limites du BMS, des câbles, des connecteurs, et des fusibles.)

Essential formulas

\(P_{el}=U×I\)
\(P_{mec}=C×ω\) ou \(P_{mec}=C×(2π× \frac{n}{60})\)
\(E=P×t\)
\(F_{traction}=\frac{r_{roue}}{C_{jante}}\)

Common errors

Confondre W (puissance), Ah (capacité) et Wh (énergie) ; oublier la conversion n → ω (rad/s) dans P=C×ωP = C \times \omegaP=C×ω.
Neglecting the efficiencies of the chain and the start-up peaks.
Undersizing the cable cross-section (high I) and ignoring the torque settings.

To learn more:

*: The technical information presented in this article is provided for guidance only. It does not replace the official manuals of the manufacturers. Before any installation, handling or use, please consult the product documentation and follow the safety instructions. The site Torque.works cannot be held responsible for inappropriate use or incorrect interpretation of the information provided.