The Physics of Flight

A multirotor flies by pushing air down. Four propellers each generate thrust $T_i$, and the vehicle responds to the total. The single most important number in a build is the thrust-to-weight ratio (TWR).

Thrust-to-weight ratio

If the four motors together can produce a maximum static thrust $T_\text{max}$ and the all-up weight (AUW) of the craft is $m$, then:

$$\text{TWR} = \frac{T_\text{max}}{m \cdot g}$$

where $g \approx 9.81\ \text{m/s}^2$. A craft with $\text{TWR} = 1$ can just barely hold itself in the air; it cannot accelerate upward. Useful rules of thumb by drone type:

Drone type	Typical TWR	Feel
Cinematic / heavy	2 – 3	Smooth, planted
Freestyle 5″	8 – 12	Punchy, responsive
Racing 5″	12 – 14+	Violent acceleration
Tiny whoop	3 – 5	Floaty, forgiving

Hover throttle

The fraction of total available thrust you spend just to stay level is the hover point. Since thrust is roughly proportional to the square of throttle command in the mid-range, a craft with $\text{TWR} = T_\text{max}/(mg)$ hovers near:

$$\text{throttle}_\text{hover} \approx \sqrt{\frac{1}{\text{TWR}}}$$

So a 5″ freestyle quad with $\text{TWR}=9$ hovers at roughly $\sqrt{1/9} \approx 0.33$, i.e. ~33 % throttle — which is why those quads feel like they have so much headroom on tap.

How propeller thrust scales

From momentum (actuator-disk) theory, the static thrust of a propeller scales with air density $\rho$, propeller diameter $D$, and rotational speed $n$ (in revolutions per second) approximately as:

$$T \approx C_T \, \rho \, n^2 \, D^4$$

Two consequences dominate FPV intuition:

1. Thrust grows with the square of RPM. Doubling motor speed roughly quadruples thrust (and demands far more current).
2. Thrust grows with the fourth power of diameter. Going from a 5″ to a 7″ prop is a much bigger jump in thrust — and drag — than the number suggests.

The power path

Energy flows from the pack to the air in a fixed chain. A fault anywhere in it shows up as poor thrust, heat, or desyncs:

A worked example

Suppose a 5″ freestyle build has:

• All-up weight: $m = 0.55\ \text{kg}$
• Measured bench thrust, all four motors: $T_\text{max} = 4800\ \text{g} = 4.8\ \text{kg-f}$

Converting to newtons, $T_\text{max} = 4.8 \times 9.81 \approx 47.1\ \text{N}$, and weight $m g = 0.55 \times 9.81 \approx 5.4\ \text{N}$. Then:

$$\text{TWR} = \frac{47.1}{5.4} \approx 8.7$$

and the hover point is $\sqrt{1/8.7} \approx 0.34$, about 34 % throttle — exactly the lively-but-controllable range you'd want for freestyle.

note

Bench ("static") thrust is always higher than thrust in fast forward flight, where the prop is already moving through the air. Treat these numbers as an upper bound for sizing, not a promise.