Barometers, airspeed and rangefinders

Why this matters

GNSS gives altitude less well than horizontal position, so drones use a barometer to measure height from air pressure. A fixed-wing drone must know its airspeed so it does not stall by flying too slowly, and landing or flying low over crops needs a rangefinder to measure distance to the ground directly. All three sensors rely on the physics of air, so they are affected by temperature and weather in ways you must understand.

Barometers and the standard atmosphere

Air pressure falls with height. The U.S. Standard Atmosphere, 1976, which matches the ICAO standard atmosphere in the lower layers, sets sea-level values of $p_0=101,325$ Pa and $T_0=288.15$ K, with temperature falling 6.5 K per kilometre. These give the pressure-altitude formula in the formula box. Near sea level, a change of 1 hPa is about 8.3 m of height.

The flight controller uses relative altitude above the take-off point, not height above sea level. But air pressure changes with the weather by several hPa within a few hours, so barometric altitude drifts on long flights. A high-resolution sensor such as Bosch’s BMP390 specifies relative accuracy of ±3 Pa, about ±0.25 m, but that figure excludes weather changes, wind blowing into the sensor port and sunlight heating the board. Builders therefore usually cover the barometer with foam and shade it.

P0, T0, LAPSE, EXPO = 101325.0, 288.15, 0.0065, 0.190263

def altitude(p_pa):
    return T0 / LAPSE * (1 - (p_pa / P0) ** EXPO)

p_takeoff, p_flight = 100800.0, 100120.0        # Pa
rel = altitude(p_flight) - altitude(p_takeoff)
per_pa = altitude(p_takeoff - 1) - altitude(p_takeoff)
print(f"height above takeoff {rel:.1f} m")
print(f"sensitivity near takeoff {per_pa * 100:.2f} m per hPa")
print(f"weather drop of 1.5 hPa looks like a climb of {per_pa * 150:.1f} m")
print(f"BMP390 relative accuracy of 3 Pa is about {per_pa * 3:.2f} m")

height above takeoff 57.0 m
sensitivity near takeoff 8.36 m per hPa
weather drop of 1.5 hPa looks like a climb of 12.5 m
BMP390 relative accuracy of 3 Pa is about 0.25 m

Airspeed from a pitot tube

A pitot-static tube has a forward-facing hole that measures total pressure and side holes that measure static pressure. Their difference is the dynamic pressure $q=\frac{1}{2}\rho v^2$ (FAA Pilot’s Handbook of Aeronautical Knowledge, flight instruments chapter). Computed with the standard density ${\rho }_0=1.225$ kg/m³, it gives indicated airspeed (IAS). True airspeed (TAS) needs the real density. On a hot Thai day, the air is thinner, so TAS is higher than IAS.

The ArduPilot guide says to cover the pitot tube at power-up, because the zero offset is measured then. The parameter ARSPD_RATIO sets the ratio between pressure and speed, and ARSPD_AUTOCAL calibrates it in flight. PX4 asks you to shield the sensor from wind, start calibration in QGroundControl, then blow into the tube tip to finish.

Rangefinders

A rangefinder measures distance from the round-trip time of a wave, $d=ct/2$. Laser types use the speed of light, which barely changes, while ultrasonic types use the speed of sound, which depends on temperature: $a=\sqrt{\gamma RT}$ (NASA Glenn). When the drone tilts, the measured range is longer than the true height and must be multiplied by $\cos \theta$ over flat ground.

import math

R, GAMMA, RHO0 = 287.05287, 1.4, 1.225

dp = 245.0                                   # Pa differential pressure from the pitot
p, t_c = 100800.0, 35.0                      # Pa, °C hot-day conditions
ias = math.sqrt(2 * dp / RHO0)
rho = p / (R * (t_c + 273.15))
tas = ias * math.sqrt(RHO0 / rho)
print(f"IAS {ias:.2f} m/s, air density {rho:.4f} kg/m^3, TAS {tas:.2f} m/s")

echo = 0.00583                               # s sound round-trip time
a20 = math.sqrt(GAMMA * R * 293.15)
a35 = math.sqrt(GAMMA * R * 308.15)
print(f"ultrasonic: assuming 20 C gives {a20 * echo / 2:.3f} m, at 35 C it is {a35 * echo / 2:.3f} m")

rng, roll = 12.0, 15                         # m laser range, degrees of roll
print(f"laser range {rng} m at {roll} deg roll -> height {rng * math.cos(math.radians(roll)):.2f} m")

IAS 20.00 m/s, air density 1.1396 kg/m^3, TAS 20.74 m/s
ultrasonic: assuming 20 C gives 1.001 m, at 35 C it is 1.026 m
laser range 12.0 m at 15 deg roll -> height 11.59 m

Module lab

Common mistakes

Summary

• A barometer converts pressure to altitude with the standard atmosphere; near sea level 1 hPa ≈ 8.3 m.
• Weather-driven pressure changes make altitude drift, so fusion with other sources is needed.
• A pitot tube measures dynamic pressure ½ρv², giving IAS; density correction gives TAS.
• Rangefinders use d = ct/2 and need compensation for temperature (ultrasonic) and tilt.

Check your understanding

1. Pressure falls by 2 hPa near sea level. Roughly how much does altitude change?
2. What is IAS for a dynamic pressure of 122.5 Pa at a density of 1.225 kg/m³?
3. IAS is 20 m/s and the real density is 1.10 kg/m³. What is TAS?
4. A laser pulse takes 100 ns for the round trip. What is the range?
5. Why does ArduPilot say to cover the pitot tube at power-up?