Things that make a difference.
Changing driving style.
Gas'n'brakes driving.
Driving at two speeds compared with one.
Energy per distance = ( F * x + F * x ) / (x+x)
= ( ( F * v * t ) + ( F * v * t ) ) / ( v*t + v*t )
= sum v**3 t / sum v t
Replace by V = ( v*t + v*t ) / ( t+t)
the time-weighted average velocity.
Get
v1=30
v2=80
t1=1
t2=1
V(v1,v2,t1,t2) = (v1*t1+v2*t2)/(t1+t2)
## energyperdistance of mixed method
Emix(v1,v2,t1,t2) = ( v1**3 * t1 + v2**3 * t2 ) / (v1*t1+v2*t2)
Eavg(v1,v2,t1,t2) = V(v1,v2,t1,t2)**2
pr Emix(v1,v2,t1,t2)
pr Eavg(v1,v2,t1,t2)
pr V(v1,v2,t1,t2)
plot [0:2] Emix(v1,v2,x,2-x) , Eavg(v1,v2,x,2-x)
plot [0:2] Emix(v1,v2,x,2-x) / Eavg(v1,v2,x,2-x)
Peak is at t1=1.5
v1=50
v2=85
t1=0.6
t2=1-t1
pr Emix(v1,v2,t1,t2)/ Eavg(v1,v2,t1,t2)
pr V(v1,v2,t1,t2)
pr v1*t1
pr v2*t2
plot [0:1] Emix(v1,v2,x,1-x) / Eavg(v1,v2,x,1-x)
If you drive 40\% of the time at 85\,mph, and
60\% of the time at 50\,mph, your average speed will be
64\,mph.
If you were able instead to drive at a steady 64\,mph,
your travel time would obviously be the same, but
your fuel consumption would be reduced by 18\%.