Flying not Floating

 

Flying not Floating

The simplest formula for calculating lift that I can find is:

 ρ v² S C_L

Where:

·         L is the lift force

·         ρ is the fluid density – originally of “air”

·         v is the velocity or “true airspeed”

·         S is the planform (projected) wing area

·         C_L is the lift coefficient at the desired angle of attack, Mach Number and Reynolds Number

https://en.wikipedia.org/wiki/Lift_(force)

(The representation of the equation got mangled and I can't be bothered to fix it)

Typical value of C_L lift coefficient is 1.5

https://www.sciencedirect.com/topics/engineering/lift-coefficient

If I assume that I want Lift force equal to the downward force, then that means the Lift I require is (Mass * local Gravity).

Do some algebra and rearrange the equation to get (looks like super and sub-scripts don’t work properly in equations with fractions):

The first term is a constant for the body in question, the second term is the inverse of the density and the third term is the inverse square of the “airspeed” velocity. Everything varies as you would expect.

Physical Properties on various bodies:

Body:	Gravity (m/s2)	Atm Density (kg/m3):	Lift for 1 kg (N):	Temp (deg C):	Atm Pressure (Bar):	Notes:
Venus	8.87	65	8.87	464	92
Earth (Air)	9.81	1.2	9.81	20	1	*
Earth (Water)	9.81	1000	9.81	20	1	*
Mars	3.72	0.020	3.72	-63	0.06
Jupiter	24.8	1.2	24.8	-70	10	*
Saturn	10.44	1.2	10.44	-139	1	*
Titan	1.35	53	1.35	-179	1.5

 

Notes:

(*)          Atmospheric density on a gas giant can be anything you choose it to be, depending on altitude/depth.

Calculate the “factor” for all the different bodies

Body:	L/CL:	Inverse Density:	“Factor”:
Venus	5.91	0.154	0.910
Earth (Air)	6.54	0.83
Earth (Water)	6.54	0.001
Mars	2.48	50
Jupiter	16.53	0.83
Saturn	6.96	0.83
Titan	0.90	0.94

 

 (Originally 17th July 2021)