A deep dive into the Cessna 172 POH showed a remarkable linearity between rate of fuel consumption and velocity at various cruise power settings ranging from 55 to 75%. Originally a study of propeller efficiency, it lead to an observation of the drag equation:
Drag = $\rho$ × Area × Cdrag × V$^2$
Power has the units kg V$^2$/time. Fuel as potential energy has the units kg V$^2$, and it's use rate as kg V$^2$/time.
Power is also expressed as Force × distance/time or kg V/s x V.
At steady state thrust force = drag force.
Examination of the drag equation $\rho$×AxCd×V$^2$ seems at first to imply Power is proportional to V$^3$.
Yet, when the units of the drag equation were written out, it was found that, in order to yield force kg velocity/time there could be only one V!
Running through the units revealed that "kg" must come from kg/m$^3$ $\rho$ × m$^2$ Area × m distance, leaving V/s as the remainder of the Drag force kg V/s.
The implications are that parasitic drag increases linearly with velocity, rather than exponentially, as often depicted, and that drag in terms of V$^2$ is actually an expression of Force × Distance or Work.
Consideration of density kg/m$^3$ x Volume of Air m$^3$ (as Area m$^2$ x distance m) has me wondering is the drag force equation being misunderstood as a Work equation?
A possible source of confusion is that, at airspeed "behind the power curve" (slow), induced drag surely makes the drag curve look exponential. But the Cessna data makes the fuel consumption kgV$^2$/s perfectly proportioned between drag kgV/s and airspeed V at cruise speeds. Not V$^3$!
Many people sing songs of praise for cruise climb, and indeed, lowering Angle of Attack and using greater speed seems to help fuel economy. What's going on here?
I will gladly migrate to physics if no one here would like to try to explain this.