practical best range application?

On Mon, 31 Jan 2005, xerj wrote:

let's say you're in flight in a normally aspirated prop plane, your
destination is blown up, your alternate is unservicable for some reason
or other and you need to stretch the fuel you have the farthest distance
possible.

Wouldn't it simply be your airplane's best glide speed? Or am I missing
something?

Of course if you can't avoid fighting a headwind, you'd have to do some
math with ground speed vs. fuel consumption at some higher airspeed to
find max range. Or is that what you're looking for?

-Dan

Wouldn't it simply be your airplane's best glide speed?

It would be the same AoA, but not necessarily the same speed. This speed
also varies with density altitude and weight.

What prompted these questions is thinking "O.K. what if this actually
happened in the cockpit without the luxury of power curve charts and a place
to go work it all out for a ten minutes".

I do not know anyway to determine this from inside the cockpit unless
you have ground distance covered and fuel flow data on the panel...
Best thing is to work this out before hand... Use your GPS (wonderful
research instrument) for distance measurements... Take off with one
test tank carefully filled to a specific mark, using the non test
tank... Pick the best range setting from the book, pick a start point
on the ground, switch to the filled tank at the start point, and make a
square pattern run (4 sides) for five to ten minutes per side, switch
off the test tank when again at the start point... Land... Fill the
test tank... Do your calculations... Now you have a data point to start
from... Pick a slightly higher or lower power setting and repeat the
test... Now you will know whether you are improving or not, and adjust
your next run accordingly... After three or four runs you will have a
good idea where the peak of the range curve occurs... Of course, a
different altitude and temperature and wing loading will change it a
few percent, but you will be as close as you can get in the real world
if you ever have to do it for real... Besides, this testing gives you
a reason to go flying other than the $100 hamburger run...

On Mon, 31 Jan 2005, xerj wrote:

Wouldn't it simply be your airplane's best glide speed?

It would be the same AoA, but not necessarily the same speed. This speed
also varies with density altitude and weight.

hmm, AoA... Well just off the top of my head here, someone please correct
me if I'm wrong...

Stall speed, of course, also depends on AoA, not speed. So, if you have
an idea what stall speed does at different weights & density altitudes,
best glide speed should follow the same curve. Best glide is the point at
which overall drag is lowest, so it stands to reason it's also where max
range would be. If you can't avoid a headwind you may need to speed up a
bit to get the best ground speed per fuel burn, but that's a simple
calculation using ground speed & a close estimate of fuel burn.

So it seems, in practice, one should be able to get really close to max
range speed very quickly without any complicated calculations.

-Dan

Wouldn't it simply be your airplane's best glide speed?

It would be the same AoA, but not necessarily the same speed. This speed
also varies with density altitude and weight.

hmm, AoA... Well just off the top of my head here, someone please correct
me if I'm wrong...

Stall speed, of course, also depends on AoA, not speed. So, if you have
an idea what stall speed does at different weights & density altitudes,
best glide speed should follow the same curve. Best glide is the point at
which overall drag is lowest, so it stands to reason it's also where max
range would be. If you can't avoid a headwind you may need to speed up a
bit to get the best ground speed per fuel burn, but that's a simple
calculation using ground speed & a close estimate of fuel burn.

So it seems, in practice, one should be able to get really close to max
range speed very quickly without any complicated calculations.

-Dan


You are correct in your implicit suggestion that these airspeeds are based upon
angle-of-attack. Maximum range glide speed and maximum endurance speed are the
same since they both occur at (C_L/C_D)max AOA. However, your statement, " . .
.. so it stands to reason it's also where max range would be . . . " is
incorrect. Maximum range speed occurs at ((C_L)^1/2 / C_D)max AOA. Thus, it
is higher than (C_L/C_D)max airspeed. Maximum range and maximum endurance
airspeeds do not occur on the same point on the performance chart.



Kurt Todoroff


Markets, not mandates and mob rule.
Consent, not compulsion.

On Tue, 1 Feb 2005 at 19:44:36 in message
, Kurt R. Todoroff
-ON wrote:
You are correct in your implicit suggestion that these airspeeds are based upon
angle-of-attack. Maximum range glide speed and maximum endurance speed are the
same since they both occur at (C_L/C_D)max AOA. However, your statement, " . .
. so it stands to reason it's also where max range would be . . . " is
incorrect. Maximum range speed occurs at ((C_L)^1/2 / C_D)max AOA. Thus, it
is higher than (C_L/C_D)max airspeed. Maximum range and maximum endurance
airspeeds do not occur on the same point on the performance chart.

This interests me. Can you point me to the maths that produces this
result? I cannot see at the moment why maximum range should not occur
at maximum lift/drag: apart from some smaller effects like the effect of
engine thrust on lift etc. and any effects where engine and/or propellor
efficiency has a significant effect.

Maximum endurance for a glider occurs at minimum sinking speed which is
normally closer to the stall AoA than maximum Lift/Drag. Maximum range
for a glider occurs at maximum Lift/Drag as you say (I think that's what
you mean), but maximum endurance does not, as far as I can see.

I presume the calculation assumes a linear relation between AoA and CL?

Your last sentence in your paragraph above, with which I agree, seems to
contradict your second sentence.
--
David CL Francis

On Tue, 1 Feb 2005 at 19:44:36 in message
, Kurt R. Todoroff
-ON wrote:
You are correct in your implicit suggestion that these airspeeds are based
upon
angle-of-attack. Maximum range glide speed and maximum endurance speed are
the
same since they both occur at (C_L/C_D)max AOA. However, your statement, "
. .
. so it stands to reason it's also where max range would be . . . " is
incorrect. Maximum range speed occurs at ((C_L)^1/2 / C_D)max AOA. Thus,
it
is higher than (C_L/C_D)max airspeed. Maximum range and maximum endurance
airspeeds do not occur on the same point on the performance chart.

This interests me. Can you point me to the maths that produces this
result? I cannot see at the moment why maximum range should not occur
at maximum lift/drag: apart from some smaller effects like the effect of
engine thrust on lift etc. and any effects where engine and/or propellor
efficiency has a significant effect.

Maximum endurance for a glider occurs at minimum sinking speed which is
normally closer to the stall AoA than maximum Lift/Drag. Maximum range
for a glider occurs at maximum Lift/Drag as you say (I think that's what
you mean), but maximum endurance does not, as far as I can see.

I presume the calculation assumes a linear relation between AoA and CL?

Your last sentence in your paragraph above, with which I agree, seems to
contradict your second sentence.
--
David CL Francis


Hi David,

I did a Google search on the contiguous string "maximum range airspeed". You
must include the quotation marks. Google returned many websites. The first
one:

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

is excellent.

In the section titled "Performance Charts", notice that maximum range airspeed
and maximum endurance airspeed occur at different locations on the drag polar.
This is a function of AOA. Also notice the language "To maximize the
endurance, we want to maximize the amount of time that we can stay in the air."
Whether you want to maximize your aircraft's endurance (time) during powered
flight or in a power-off gliding descent (even in a glider), the principal is
the same. You want to operate the aircraft at an airspeed that corresponds to
(C_L/C_D)max. This is not close to the stall angle of attack.

My two sentences in question are consistent.

I hope that the link that I provided helps.

Best wishes.



Kurt Todoroff


Markets, not mandates and mob rule.
Consent, not compulsion.

I'm confused too.

This is the sentence:-

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

How can they be "the same" when they occur at two different points on the
power curve?"

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