Hi Kirk,

http://www.eaa1000.av.org/technicl/p...s/perfspds.htm

I did look at that site and it is jolly and the rough equations are
correct but presented perhaps as more complicated than they need be.

Leaving out some constants:

Power = drag( or thrust) x velocity.................................(1)

Velocity =
distance/time.............................................. ..(2)

Total Energy = thrust (or drag) x distance travelled...........(3)
equivalent to total fuel used.

Since from (2) distance = velocity x time.

(3) can be re-written as energy = thrust x velocity x time

which is the same as

Total energy = Power x
time............................................(4 )

Fuel used is SPC x time x power

Fuel used = SPC x time x thrust x velocity
Fuel used = SPC x time x thrust x distance /time
Fuel used = SPC x thrust x distance..................................(5)

Therefore since SPC is a constant then (5) is equivalent to (3).

Now this will change with time as fuel is burned up this effect is
significant on long range airliners because the required lift = weight.

So calculating the range does require an integration but at all times
the drag (and thrust) will be least when the aircraft flies at Maximum
Lift drag ratio because it will then be the least fraction of the
weight.

So you fly at maximum Lift/Drag and get maximum range. As you fly you
adjust your speed to stay at maximum Lift/Drag.

This seems in agreement so far with the WEB site that you quoted.
However I have a little difficulty getting my head around the 'optimum
cruise' that the site goes on to deal with.

The actual graph of power against velocity does show the minimum value
of power/velocity clearly.

Quoting from the Web site:

He gets to

[(lb of fuel)/nm proportional to Power/V]]

All OK but I am now going to use V for speed, Time for hours and dist
for distance.

Now our friend goes on to decide that fuel flow per unit V is the right
parameter for optimum cruise speed.

Why is that an optimum cruise?

He starts with lb of fuel per distance as proportional to Power/V

But what is Power/V? Nothing more than thrust again which is also drag.

And the left hand side can be changed by letting dist = V x time

Now we have (lb of fuel)/(V x time) proportional to thrust

Now he divides by V again to get (cancelling a bit)

(lb of Fuel)/time proportional to Thrust/V

So in effect he is finding the 'optimum' of (lb of fuel per hour) in
terms of thrust per knot. Why is that an optimum?


My two sentences in question are consistent.

Hmm. First sentence: "Maximum range glide speed and maximum endurance
speed are the same since they both occur at (C_L/C_D) Maximum AOA."

Second sentence: "Maximum range and maximum endurance
airspeeds do not occur on the same point on the performance chart."

Those do not mean the same thing to me. Combine the two and we have that
the speeds are the same but do not occur at the same place on the
performance chart. How could that be? It seems to me that the first
sentence is wrong - Maximum range glide speed and maximum endurance
speed are NOT the same as is confirmed on the Web site.

I hope that the link that I provided helps.

It did - up to a point!

E&OE
--
David CL Francis