The Physics of flying an autonomous drone 90 mph (Record 1)
Alright, it's finally time to put what I've learned from Khan Academy physics to good use. Using the laws of forces and the fundamentals of kinematics, I calculated how fast my drone must accelerate in order to reach an average speed of 90 mph in just 100 meters. It is important to note that these calculation are based on the assumption that average velocity will be evaluated instead of maximum or final velocity.
A aircraft has 4 major forces. Thrust, lift, drag, and gravity. Drones use their thrust to produce lift, while airplanes use the shape of their wings to create lift, so in the diagram above I have listed only thrust. The thrust vector is slightly pointed upwards as it will also be propelling the drown upwards, against the force of gravity.
Now, let's look at the requirements that led me to the conclusion I would need to achieve an acceleration of 35.3 meters/sec^2.
According the second record I will be attempting, the drone is required to make two 100 meter passes, and its final velocity will be recorded, and the record will be the average of the two passes. For the first record I will be attempting, I was not able to fid the requirements, but i assumed that it would instead target average velocity. Furthermore, I can attempt both records with the same drone because the acceleration to reach a final velocity of 185mph, which is my target for this drone, is about the same.
If we were to travel 100 meters at an average velocity of 42 meters/second (90 mph), we would be traveling for 2.38 seconds. We can use these known variables in the kinematic equation below to calculate the value for a, our acceleration.
We can use the same equation with different known variables to calculate what a safe starting altitude is if we were to let this drone plummet to the ground without any lifting force. I rounded up the time value to add a safety buffer (which was a little overshot) and calculated that a safe starting height is about 40 meters. This is plenty of heigh considering that the air friction was not considered and that the flight time is actually shorter.
So, what do these calculations show us? Well, we need to create a drone that will have a net acceleration fo 36 m/s^2 in the x direction. Will we be able to achieve that?