Why a drone hovers: thrust equals weight

TL;DR:

• A drone hovers when the total upward thrust equals its weight, T = m g, so there is no net force and no acceleration.

• For a 1.2 kg drone, the weight is about 11.8 N, so each of four propellers supplies about 2.9 N in a hover.

• A drone needs thrust well above its weight to climb, maneuver and handle a sagging battery. Tilting to move forward needs more total thrust.

A hovering drone looks calm, but it is working hard. Nothing is moving, yet four propellers are throwing air down all the time. The reason is simple: gravity never stops pulling, so the drone has to push back with exactly the same force.

Newton's second law at work

Newton's second law says that the net force on an object equals its mass times its acceleration: F_net = m a. For a drone, two vertical forces act: the thrust T upward and the weight m g downward. The net upward force is T − m g.

If T = m g, the net force is zero, so a = 0: the drone neither rises nor falls. That is a hover. If T > m g, the drone accelerates upward; if T < m g, it accelerates downward. Hovering is not a special state. It is just the thrust that balances the weight.

Worked example: a 1.2 kg drone needs about 11.8 N of thrust

Use g = 9.8 m/s².

1. Weight: m g = 1.2 × 9.8 = 11.76 N, which is about 11.8 N.

2. Thrust per propeller in a hover: 11.76 / 4 = 2.94 N.

3. Climb: suppose the propellers together produce 14.0 N. The net force is 14.0 − 11.76 = 2.24 N upward, so a = 2.24 / 1.2 = 1.87 m/s².

4. Descend: with only 10.0 N, the net force is 10.0 − 11.76 = −1.76 N, so a = −1.76 / 1.2 = −1.47 m/s², accelerating downward.

Check: the climb with 14.0 N has a net force of 2.24 N and mass 1.2 kg, so 1.2 × 1.87 = 2.24 N. It is consistent.

Thrust margin

If the propellers could only produce 11.76 N at full power, the drone could hover at full throttle and nothing else. It could not climb, resist a gust or recover from a tilt. Designers specify a thrust-to-weight ratio, the maximum total thrust divided by weight. A common target for a stable, controllable multicopter is 2 or more (a rule of thumb, not a law). For our drone, a ratio of 2 means a maximum thrust of 2 × 11.76 = 23.5 N, or 23.5 / 4 = 5.88 N per propeller, and the hover then needs only half of full throttle.

That headroom is what the flight controller uses to change the speeds of individual propellers to roll, pitch and yaw (see how a quadcopter flies). If the motors are already at their maximum for a hover, there is nothing left for steering.

Tilting to fly forward

To move forward, the drone tilts, so the thrust vector leans. The thrust T is along the drone's vertical axis, so when the body tilts by an angle θ, the vertical part is T cos θ and the horizontal part is T sin θ. To hold height while tilting, the vertical part must still equal the weight:

T cos θ = m g, so T = m g / cos θ

At θ = 20°: T = 11.76 / 0.9397 = 12.52 N. The horizontal force is m g tan θ = 11.76 × 0.3640 = 4.28 N, and the forward acceleration is 4.28 / 1.2 = 3.57 m/s² (before air drag, which grows with speed and limits the top speed). So tilting at 20° requires about 12.52 − 11.76 = 0.76 N more total thrust than hovering. The steeper the tilt, the more thrust it takes to keep the height.

Battery effects

• Weight: the battery is a big share of the mass. A larger battery gives more flight time but needs more thrust to hover.

• Voltage sag: as the battery discharges, or when it draws a large current, its voltage falls. Motor speed and thrust for a given command fall with it, so the same throttle gives less thrust later in the flight.

• Current: hovering draws a steady current. Maneuvers draw more. A battery that cannot supply the peak current sags more, as explained in batteries for robots.

• Cold: a cold battery sags more.

Where it goes wrong

• Wrong mass. Forgetting the camera, the battery or the cables gives a weight lower than the real one.

• Thrust figures from marketing. Use measured thrust for your propeller and voltage, from a datasheet or a thrust stand, not just a quoted maximum.

• Ground effect and air. Near the ground or a wall, airflow changes thrust a little. In thin air at high altitude, thrust drops.

• Hover at nearly full throttle. Then no spare power. Add thrust or remove weight.

• Assuming a stable hover. Equal thrust and weight is necessary but not sufficient. Without feedback, the drone tilts and drifts (see drone flight controllers and stabilization).

Safety: Do not test thrust with propellers spinning near your hands, face or loose clothing. Use a test stand that holds the drone, wear eye protection, and keep other people away. Never run motors at full power on the bench for longer than a short burst, because motors and speed controllers overheat. Handle LiPo batteries with care and use a proper charger.

Try it yourself

Weigh your drone with its battery, in kilograms. Multiply by 9.8 to get the hover thrust in newtons, and divide by four for each propeller. Look up the maximum thrust for your motor and propeller at your battery's voltage, and compute the thrust-to-weight ratio. Then estimate the share of full propeller speed a hover needs, which is roughly the square root of the fraction of maximum thrust, because thrust grows with the square of speed. Compare with the hover throttle your flight log shows.

Frequently asked questions

Why does a drone need more than hover thrust?

Extra thrust lets it climb, tilt and counter gusts. It also covers battery sag, which reduces thrust late in the flight.

Does tilting the drone change the thrust needed?

Yes. The vertical part of the thrust must still equal the weight, so total thrust must rise by a factor of 1 / cos θ.