Here are a couple of posts from the archive on the subject. see what you make of them.
no sponsor31st Oct 2004, 14:41
It is a very complex subject. Work this out, and you will nail the Perf exam, and a good bit of PoF.
VMD - Minimum Drag. Found on the drag curve, at the bottom. Best speed for Endurance (Jet) Minimum glide angle, and it is also where CL:CD is at a maximum, or CD:CL is at a minimum. Look on the drag curve and you'll see it is at the point where induced and profile drag cross. It is also equal to a bunch of other things, such as Vx for a Jet, and V4 (v2+10).
VMP is min power. So you need to look on the power curve. It is at the bottom on the power req curve. Here you want to use as little fuel as possible, so for the prop it will be almost near Vs, and very much in the speed unstable regime. This is where gliding for endurance for Prop and Jet will be. If you want to find VMD, it will be at a tangent on the pwr req curve. So you can conclude that VMP is slower than VMD.
Best speed for range will be at the tanget of a line from the origin which just touches the drag curve. It will be at 1.32 Vmd. Most jets will fly a little higher than this at 1.37 Vmd, since it equates to 99% range, but an increase in 4% speed, which makes it better economically.
What you will need to know for the exam is how these things change. What happens to VMD as a EAS and as a TAS at altitude?
Beware that the Power curve is in TAS and drag in EAS, so all EAS speeds don't change, but TAS speeds do as you get higher. So, you need to learn the inter-relationships between EAS, RAS, TAS and Mach numbers. Remember ERTM - if EAS is constant and you climb, then RAS, TAS and Mach will all increase.
If you can figure out profile and induced drag, and how these are affected by flaps, increases in mass etc, then you will be well on your way.
As I said, it's complex. Try the book, 'Performance' by Swatton.
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Keith.Williams.31st Oct 2004, 15:03
VMP is the speed at which the power required in minimum
VMP is also the speed at which propeller aircraft endurance is greatest. This is because fuel flow in propeller aircraft is proportional to power. So by flying at the minimum power required speed we use the minimum fuel flow. Using minimum fuel flow maximises the time it takes to burn the fuel on board.
VMP is also the speed at which the glide endurance is greatest. This is because in flight the aircraft expends energy moving forward against the drag force. The total energy of the aircraft is the sum of its kinetic energy (1/2m Vsquared) + potential energy (weight x height). In powered flight this energy is constantly being replenished by the engine. But if we shut down the engine and glide, the stored energy cannot be replenished. So as we glide we gradually use up the stored energy. When we are stoped on the ground we have used up all of the stored energy. So for maximum glide endurance we must use up the stored energy as slowly as possible. Energy useage rate is power required. So for maximum glide endurance we must fly at the minimum power required speed (VMP).
VMD is the speed at which total drag is least. It is also the speed at which we achieve:
a. Best propeller aircraft range.
b. Best glide range.
c. Best jet aircraft endurance.
We can find Vmp from a power required curve by drawing a tangent from the origin to the curve. This will touch the curve at Vmd. We can find Vmp from a drag curve by drawing a straight line from the origin to hit the curve at 90 degrees. The line will cross the curve at Vmp. If you do this a few times you will find that Vmp is always less than Vmd.
If you want an easy way to remember how to find the speeds for best range and best endurance for props and jets just remember the terms:
"P for Power P for Props" and "D for Drag D for Dyets".
For prop aircraft "P for Power P for Props" means that you sketch the curve for power required against airspeed. It looks a bit like a Nike tick. If you draw a horizontal line to just touch the bottom of the curve, it will touch it at Vmp. This is the speed for best prop endurance. Now draw a straight line from the origin to just touch the curve. It will touch it at Vmd which is prop best range speed. The horizontal line gives best endurance and the tangent give best range.
For a Jet just do the same but this time use the drag curve. (D for drag D Dyets). The horizontal line will touch the bottom of the drag curve at Vmd which give best jet endurance. The tangent drawn from the origin touches the curve at about 1.32 Vmd which is best Jet range speed. Once again the horizontal line gives best endurance and the tangent gives best range.
For the ATPL exams it is also worth noting that best glide endurnce means lowest rate of descent. They sometimes use the terms "Vmsr, Velocity minimum sink rate" or "Vmdr , Velocity Minimum descent Rate" insted of Vmp. When gliding at maximum range speed your glide angle will be minimum so they sometimes use the term "Vmga, Velocity Minimum Glide Angle" instead of Vmd.
I'm with you guys. I can't quite see why the Power Required, Thrust Required, and Total Drag curves are not the same, assuming we are using the same speed, ie. IAS, TAS, CAS, etc. and, perhaps because I cant see that, I dont understand how VMD can be the speed for Max Range. Maybe someone smarter than us will come up with an explanation that us simple folk can grasp!
MJ
