Airplanes on Mars?

In a word,  probably not. 

The mechanics required for steady flight are illustrated in Figure 1 below.  Basically,  lift must balance weight,  and thrust must balance drag.  For clarity,  the moment balance about the center of gravity is not depicted. 

Lift and drag are both proportional to the wind pressure and the wing area.  The coefficients of proportionality are the lift and drag coefficients.  Control of lift is by angle of attack (AOA),  and the usable lift coefficient only varies between zero and the stall value (a bit over 1).  For control purposes,  the same basic lift coefficient values must be used on Mars as on Earth.

The wind pressure (q, the dynamic pressure) is proportional to density and to velocity squared.  The density can be calculated as a density ratio (σ) multiplied by a standard density value (ρ_o).  Earth sea level density on a standard day is the usual value used for that standard density.  Values are shown. 

Under ideal gas assumptions (P = ρ R_univ T/MW),  the density ratio pretty much anywhere is the pressure ratio to Earth standard pressure,  multiplied by the molecular weight ratio to standard,  and divided by the absolute-scale temperature ratio to standard.  For typical pressures and temperatures on Mars,  density ratio is near 1% of Earth sea level,  but this is quite variable since the “air” pressure there is quite variable.  An average value is shown.  Surface gravity on Mars is 38% that on Earth.  

To design aircraft for Mars,  we need the surface density ratio divided by the surface gravity ratio.  The net effect is that the levels of the aerodynamic forces acting on a reduced weight on Mars, are about factor 35 smaller than here on Earth,  at otherwise the same AOA’s!  That factor can increase either the wing area or the square of the velocity,  or some of both,  to get the same balance for steady flight on Mars. 

Note that if you make the wing bigger,  it will be more massive in proportion to that increased area,  and therefore heavier,  even in the lower gravity of Mars.  The weight increase of more wing area will act toward overcoming any lower speed benefit.  That is because the density effect is much larger than the reduced gravity effect,  on Mars.

Velocity squared factored up by 35 is the same as velocity factored up by almost 6.  Example:  if landing and takeoff speed for some airplane design was about 100 mph on Earth,  it would be almost 600 mph on Mars for the same wing area as on Earth.  Such speeds that close to the surface are quite dangerous.  That is just not something to be attempted voluntarily. 

Double the pressure to 12 mbar in the Hellas Basin,  and the over-100 density reduction factor halves.  That density ratio divided by the gee ratio is now closer to 17 than 35,  and its square root is a velocity ratio a bit over 4.  It’s still a bigger,  heavier (and impractical) wing by a factor of 17 on wing area,  or else a speed near the surface exceeding 400 mph.  Or something in-between,  with an impractically-large wing and a speed that is still too high close to the ground to be safe.  Not at all safe to attempt. Plus,  you cannot fly it anywhere except down in that basin.

The same basic aerodynamic and weight-carried factors act on helicopter rotors in pretty much the same way.  This is why I think the use of airplanes (or helicopters) as we know them here on Earth,  at a size scale suitable for transporting freight or people,  are simply not technologically feasible in the extremely thin “air” of Mars,  despite the lower gravity. 

Not absolutely impossible,  but a practical design configuration is pretty much unimaginable. 

Figure 1 – First Cut Exploration of Aircraft Design Requirements for Mars

Second,  Closer Look:

Now,  looking at this issue a bit more closely,  let us explore landing and takeoff speeds that are practical,  and at lift coefficients that are high,  but with adequate stall margin,  sort of like what is required by the FAR’s here on Earth.  For that,  I presume 120 mph = 176 ft/sec = 53.6 m/s,  and a max lift coefficient at takeoff and landing of 1.0.  I also looked at high altitudes on Earth,  and at higher pressure in the Hellas Basin on Mars.  I did this with a spreadsheet,  as illustrated in Figure 2 below.

Those numbers for Mars might not seem too bad,  until you try to sketch what that kind of a change to an aircraft design might look like.  I did that in Figure 3 below,  holding the fuselage size constant,  and just up-sizing the wings and tails.  There is no way to get the required tail arm lengths for stability and control,  without also up-sizing the fuselage,  which drives up mass even further!  It would be the same with a swept-wing design for higher cruise speeds:  you still have to land and take off!  

That should indicate just how impractical it will always prove to be,  to design conventional airplanes capable of safe and practical flight on Mars,  regardless of the propulsion.  That “air” is just too thin!

Figure 2 – Sizing Wings for 120 mph Takeoff/Landing Speeds on Mars

Figure 3  -- Upsizing Aerosurfaces for Fixed Fuselages For Mars