Flight equations

[youness fouqani]

Hi there !

I am trying to build my own quadcopter from A to Z. I mean I will build everything myself except for the engines.

So far, by using newton laws, I got these equations :
(notice : I am totally neglecting air drag but not sure if that right at quad speed range).
By plugging these equations into an arduino, we could control each engine force (Fe) , then converting that force into required RPM ??

1. reach a vertical speed :
Fe = m/4((v-v0)/t) + g)
m: quad mass
v : actual speed
v0 : velocity to reach
t : time to reach v0

2. Hover
Fe = 1/4 * (m . g)
g : gravity

3. Displacement
Fe = 0.25 * (m/sin(O)) *((v-v0)/t + g)

where O = tan-1(( ((v-v0)/t) + g) / ((v-vs)/t2 + g) )

v : actual speed
v0 : vertical velocity to reach
vs : speed to reach
t : time to reach v0
t2 : time to reach vs
O : angle of tilt


I have the following questions :
Is these equations right ?
Could I control engines without ESC ?
Should I neglect air drag ?
How to convert Fe to RPM based on engine and props specs ?

thanks for reading and replying.

 

[Bill Safrit]

No you cannot control the motos without ESCs. If you are going for as much speed as you can get out of your project drag is an issue with every single aircraft ever designed. Fe? A motor is not an engine. The correct term you are trying to get at is Kv. (1000 rpm per volt) Kv is how all brushless motors are rated. Go to this page and download one of the Scorpion motor calculators. http://www.scorpionsystem.com/downloads/ Scorpion outrunners are one of the highest quality outrunner motors on planet earth. As far as prop choice, go with the benchmark recommended prop suggested by the maker of the motor. The best performance can be obtained with carbon fiber props. A lot of guys will mount a cheap APC prop to a motor. Spend a little more money and buy a better prop. Example. A CF prop can be expensive. On the other hand an inexpensive Xoar beechwood prop will far out perform an APC nylon prop. Hope this helps.