PERF/POF: Vmp - Vmd (Again)

[All-The-Nines]

I know I know....this gets repeated every 6 months or so on here (a search of the forums gave me 5-6 threads to read through) however unfortunately none of them, and not even Google seem to be able to help me.

I don't know what it is - so far everything else I've read in POF/PERF makes sense. But I seem to have hit a wall with this particular area, I must be missing a very simple piece of the jigsaw which would make it click.

I could of course learn the answers in the question bank, but I absolutely hate leaving a topic without fully understanding it and hence why I'm here for a bit of help.

Firstly, how/why is Vmp less than Vmd, in practical terms what is the difference?

One thing I don't really understand in my textbook (Oxford) is how it goes in to a long drawn out explanation of how to calculate Vmp...but on the next page immediately tells you that Vy for a jet aircraft is 1.32Vmd. Where does the 1.32 come from, and how is this related to Vmp according to the prior explanation? It doesn't seem like there was any point in explaining Vmp to me - but there must have been otherwise this whole thing might have made sense.

Lastly, we are told in the glide that Vmp gives the the lowest rate of descent. Again in layman's/practical terms, could someone please explain how this comes to be the case? We are told that in the glide, we simply need to balance the drag with the value of W cos y (I'm using y here for Gamma). This would therefore make me come to the conclusion that the less Drag, the less the value of W cos y needs to be. How can it be that there is a speed (Vmp) which is higher up the Drag curve than Vmd, which would give us a lower descent rate? I might be making this too complicated for myself, I'm just struggling to see how any extra Drag above Vmd in a glide descent could possibly be a good thing.

I think that's all that's confusing me for now, apologies if this all seems a bit simple but I just want to get the basic principle clear in my head before I move on.

Thanks in advance to anyone that may be able to help!

[Lightning Mate]

Lastly, we are told in the glide that Vmp gives the the lowest rate of descent.
Again in layman's/practical terms, could someone please explain how this comes
to be the case?

Any descent is a conversion of potential energy into kinetic.

Gliding at the minimum RATE of descent requires this energy conversion to be at the lowest possible RATE.

RATE of doing work is defined as POWER.

Therefore the speed which must be used is minimum POWER speed. :)

[bravobravo74]

Drag is a force whereas power is the product of thrust and speed. Power required at Vmp is less than the power required at Vmd however the drag at Vmp is greater than that at Vmd. In practical terms (assuming a propeller-driven aircraft) best rate of climb, best glide range and best (still air) powered range occur at Vmd which itself gives the best lift/drag ratio. Best powered endurance and best glide endurance (minimum rate of descent) occurs at Vmp. Best angle of climb will occur somewhere around Vmp.

1.32Vmd represents the tangent to a jet's drag curve and therefore gives the best speed/drag ratio. Remember that a jet's fuel consumption is proportional to thrust whereas a propeller-driven aircraft's fuel consumption is proportional to power.

Vmp is a lower speed than Vmd. In a glide the rate of descent effectively depends on the descent gradient and the speed at which the aircraft travels along this path. Even though the descent will be steeper at Vmp than at Vmd (hence Vmd gives a better gide range) the lower speed at Vmp accounts for the lower rate of descent.

[Lightning Mate]

Vmd which itself gives the best lift/drag ratio

It is as well to remember that this is only true in level flight, not in a descent.

[Dick Whittingham]

Beware the difference between theory and practice, jets and pistons.

The power required for flight is an airframe factor as is the drag at various speeds. Vimd doesn't depend on the powerplant. Vimd is calculated from the assumption that drag is the sum of two equations, induced drag which is proportional to 1/Vsq and profile drag, proportional to Vsq. from thiswe can draw the well known drag curves and spot on them three points of interest, Vimp, Vimd and the tangent to the drag cuve at 1.318Vimd. Why 1.318? It's in the math, no more than that. For the curious the number is actually the fourth root of 3

Now your choice of speeds to fly will depend on how your energy, stored as fuel or height, will be used up. A jet uses fuel providing thrust so you get best range at 1.32Vimd and best endurance at Vimd. For a piston, that uses up fuel as power we drop down one. Pistons fly for range at Vimd and for endurance at Vimp

In a glide, as the engine is inop we don't need to differentiate between jets and pistons. Glide for range at Vimd and for endurance at Vimp - as Lightning Mate has explained

But, back to the top. these explanations rely on quite a few assumptions


Vide supra LM's caveat

[All-The-Nines]

Thank you for these answers, they are useful.

Can anyone think of a scenario where maximum glide endurance would be useful in real life commercial flying? Unless you're over the ocean with no land anywhere near gliding range and quite simply want to minimise your time in the water before the rescuers arrive? Otherwise it would seem that maximum glide range (flying at Vmd) is always going to be your best bet in that it increases your chances of making landfall somewhere, or getting as close to somewhere to land as possible.

Also, I was trying to explain an emergency descent scenario in my head and wanted to check a few things:

Let's say you were at 20,000ft and had a rapid de-pressurisation, and needed to get to 10,000ft ASAP. Maximum angle of descent would require the speed for maximum excess drag, whilst maximum rate of descent would require the speed for maximum excess power required. Which of these speeds is higher, and why? If I try to impose a graph of power required on top of drag/thrust required, I would imagine that the speed for maximum excess power required is lower than maximum excess drag. But then that doesn't quite add up when I'm thinking to myself 'surely to get down fastest you need to be flying at the steepest angle, at the fastest possible speed'.

[Alex Whittingham]

I cannot imagine a scenario where one would want minimum rate of descent, I think it is just a theoretical question.

The emergency descent profile is a compromise. Clearly the fastest initial descent would initially involve pointing the aircraft at the ground and opening the throttles, but one would hit VNE/VMO fairly quickly. Once VNE is hit it may be that the highest rate of descent is obtained clean with a high VNE or with drag devices deployed at a lower limiting speed, it depends on the aircraft.

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