Thrust:
According to AirWolf II, "A commonly used rule is that velocity of the air at the propeller is v=½Δv of the total change in air velocity."
Where,
T | Thrust which is a kind of force (F). |
D | The diameter of the propeller (m) |
ρ | Air density - approximately 1.225 kg / m3 |
v | The velocity of the air pulled into the propeller (m/s) |
Δv | The velocity of the air pushed away from the propeller (m/s) |
Next, we can relate mass to the thrust by substituting T with the function for force (Force = mass (m) x acceleration (a)) and solve for m, giving us:
In order to find mass, we need to first know Δv - this is what slowed me down for a little while. So, in order to solve for Δv without first knowing the mass, we'll need to create a second equation (power = force x velocity):
Where,
η | Efficiency of motor (approximately .75) |
W | The max wattage of the motor (W = IV or W = I2r or W = V2/r) |
C | The scaling factor from 0 to 1 (one being maximum throttle) |
m | Mass (g) |
a | Acceleration |
Δv | The velocity of the air pushed away from the propeller |
Substitute and solve for Δv:
A real-world example using this formula:
I have brushless motors that run with a max current of 10.5A at 11.1V with a prop radius of 4.5" (0.1143m). Given the following:
C: 100% | η: 80% |
ρ: 1.225 kg/m3 | D: 0.2286 m |
a: 9.8 m/s2 | W: 116.55 |
...each motor with it's mounted prop running at 80% efficiency and the throttle maxed, can carry a maximum approximate weight of 615 grams (or 0.614646... kg). Since I have 6 mounted to my chassis, my AUV will be able to support a maximum [hover] load of approximately 3.69kg. (since the motors are arranged in pairs, this number may be further increased via an increase in efficiency by re-evaluating for v given the previous solved equation)
No comments:
Post a Comment