Why is Vmd not at the bottom of the power required curve?

[Jake Didsbury]

Hello, I am a student ppl currently studying flight performance and planning.

I am looking at the cruise section, the example I have explains Vmd always occurs at the tangent of the power required curve, however this means it does not fall at the lowest point of the curve.

Power required curve is equal to drag curve? So how come Vmd does not occur at the lowest point, which would seem to be the logical thought being the minimum?

Thank you.

[FlyingStone]

I am looking at the cruise section, the example I have explains Vmd always occurs at the tangent of the power required curve, however this means it does not fall at the lowest point of the curve.

Throw this book away. For both propeller (which is what you are interested in, I presume) and jet aircraft the minimum drag speed (Vmd) occurs where at the most bottom point of the drag curve, where the drag is minimum - as the name suggests. However, unlike propeller aircraft, where maximum range speed is more or less equal to minimum drag speed, in jet aircraft the maximum range speed is approximately 30% higher (IIRC you have to multiply the Vmd with 4th root of 2 to get the exact theoretical speed, but don't hold me to it).

To simplify for propeller aicraft :

Vmd = minimum drag speed = maximum range speed = speed at which the drag is minimum = the lowest point of the drag curve

[Jake Didsbury]

Thank you this makes it much clearer for me!

The other thing I am confused with is why Vmp and Vmd are not equal. I would have expected them to be same but vmd is higher than vmp?

The first thing that comes to mind is to think that for the minimum drag the minimum amount of power would be needed

[mrmum]

I think that the simplified bit is too over simplified to be correct.
I don't have a PPL text book to hand, but IIRC, they show the drag curve with Vmd at the lowest point, this is best ENDURANCE speed, not best RANGE. Minimum drag equates to minimum required thrust and so minimum fuel burn.
The line from the origin tangential to the "power required" (drag) curve, is actually giving best range speed and will be a higher speed than Vmd.
http://t2.gstatic.com/images?q=tbn:ANd9GcRfMI-XtsV0lZLyVbeCJoEmLMMglJ-re8zGkia29RLx9mJVH_mvjw
http://t2.gstatic.com/images?q=tbn:ANd9GcRfMI-XtsV0lZLyVbeCJoEmLMMglJ-re8zGkia29RLx9mJVH_mvjw

[keith williams]

Power required curve is equal to drag curve?


The above statement is untrue. Power required is not equal to drag, it is equal to drag multiplied by TAS.


So how come Vmd does not occur at the lowest point, which would seem to be the logical thought being the minimum?


The statement above is untrue, because it is based on the first statement which is also untrue.


To demonstrate the relationship between Vmd and Vmp we need to start by sketching a drag curve. This should be a curve which is high at low speed then gradually decreases with increasing speed until it reaches a minimum value, then increases as speed continues to increase.

Now on the horizontal axis below the drag curve mark of TAS in equal increments from left to right. Then number the TAS increments 1, 2, 3, 4 etc to indicate that TAS increases from left to right.

Now above each increment draw a dot which represents the drag value (as indicated by the drag curve) multiplied by the TAS. At the left end you multiply by 1, so the curve does not move. At the next increment you multiply by two so the dot is twice as high as the drag curve. At the next increment you multiply by three so the dot is three times as high as the drag curve. When you have drawn all of the dot, join them together to form the power required curve.

Comparing the two curves you will see that the power required curve, differs from the drag curve in that its right hand end is much higher than its left hand end. The process of multiplying by gradually increasing TAS values has pushed the curve up and rotated it anticlockwise.

This anticlockwise rotation has caused the lowest point on the power required curve (Vmp) to be at a lower TAS than the lowest point on the drag curve (Vmd) curve.

No matter how many times you repeat this process, the result will always be the same. Vmp is lower than Vmd.


Any straight line drawn from the origin represents a fixed ratio of power required to TAS. A vertical line reresents infinite power required with zero TAS, so the power required:TAS ratio is infinite. A horizotal line represents zero power required and infinite TAS, so the power required :TAS ratio is zero.

The value of any ratio is the first variable divided by the second. In the case of the power required to TAS ratio its value is power required / TAS.
Power required is (Drag x TAS), so this ratio becomes (Drag x TAS) / TAS. But (Drag x TAS) / TAS = Drag. This means that the slope of any of these straight lines is equal to the drag. So the line of shallowest slope represents the minimum drag.

The power required curve represents all of the possible combinations of power required and TAS that the aircrarft can achievbe. So the minimum drag value occurs at the point where the shallowest straight line just touches the power required curve. This is at Vmd.

So Vmd occurs where a tangent from the origin touches the drag curve.

If the curves that you have sketched do not give VMD coincident with this tangential point, it simply means that your sketch of the drag curve was not a good reprsntation of Drag = ( CD 1/2 Rho Vsquared ).

[de facto]

The above statement is untrue
It was not a statement but a question...how can a question be untrue?:E

[mustafagander]

Be sure that you are very aware of the definitions of RANGE and ENDURANCE and what each means to you as an aviator.

[zepharym]

Keith,

Can you assist me to understand why the speeds for Maximum Range Power are so much higher on a B200 turboprop than the speed for best range..eg B200 performance charts have ISA SL speeds for Max Range power around 205 KIAS ..but speed for best range is only about 140-150 KIAS.

Am I missing something obvious...am I misinterpreting "Maximum Range Power" data.....or is this perhaps a function of the min idle power setting (eg 61% ) ....

:ugh:

[keith williams]

I'm afraid that I cannot help without seeing the data source. At first glance I'm puzzled by the idea that maximum range differs from best range.

[zepharym]

Perplexified ...I was...

Have a look at the attached extracts...

By my calcs (using a drag profile which matches performance data in AFM pretty well)..the speeds for best range shuld be about 150-160 KCAS depending on weight range.

Performance Speeds
http://i46.tinypic.com/1499mza.jpg

MaxRangePower Chart
http://i45.tinypic.com/2s6353k.jpg

Endurance profile
http://i45.tinypic.com/16apdow.jpg

:confused:

[keith williams]

I cannot provide any definitive answer to your question, but I can make some suggestions.

For many years the conventional wisdom has been that:

FOR PROPS
Fuel flow is proportional to power, so:
Maximum endurance occurs at the minimum power required speed (Vmp).
Maximum range occurs at the speed where the ratio of TAS to power required is maximum (Vmd).

FOR JETS
Fuel flow is proportional to thrust, and is Steady level flight thrust = drag so:
Maximum endurance occurs at the speed where drag is minimum, which (Vmd).
Maximum range occurs where the TAS to drag ratio is maximum (about 1.32 Vmd)

But the above conventions are simplifications and they assume that the fuel efficiency is constant in both cases. In reality, factors such as constant speed props and ram effect in turboprop engines, make this assumption invalid.

This means that the endurance and range performance of turboprop aircraft fall somewhere between conventional piston/props and jets. If we take your figures of 150 to 160 knots for Vmd, then the best range figure of 205 knots is about 1.32Vmd. (155 x 1.32 = 204.6)

[sycamore]

Zeph, the airspeeds quoted on the graphs are TAS,not IAS. eg,at 26000ft a TAS of 222 kts is about 148kts IAS(ISA).At sea-level IAS and TAS are nominally the same..

If you take a glance at endurance and range speeds at 25-35000ft there is only about 8-10 kts difference,and overall about 100nm loss flying at endurance speed rather than range speed..

[keith williams]

In his earlier post Zepharym said:


eg B200 performance charts have ISA SL speeds for Max Range power around 205 KIAS ..but speed for best range is only about 140-150 KIAS.



So the curosity does not appear to be simply a matter of the difference between IAS and TAS with increasing altitude.

[zepharym]

Sycamore,

I am looking at the speeds along the "x-axis" for Sea level. The speed for maximum range power curve at the SL intercept is shown as 204 -207 KIAS depending on starting weight

still :confused:.

[zepharym]

What I found was that if you draw a line across the power required curve (derived from drag polar) at about the 60% N1 torque figure ...the speed on the power required curve is ....:ooh:...about 205 KEAS...this made me wonder if the "Low Idle" setting (61%) for the B200 has something to do with it...(Im not a turboprop pilot...)

I'm also wondering if the phrase is "Maximum Range" Power or Maximum "Range Power"..which might possibly explain someting...:suspect:

[Pugilistic Animus]

Keith Williams is absolutely correct--

but don't theorize with the flight manual the engineers have already don all that for these are not simple matters, much more complex than you'd imagine...you do not have the drag polars, I can assure you; only 'They' have them!!!!...:hmm:

Read it CAREFULLY and ALWAYS do what the Flight Handbook tells you to do...The AFM always right don't make inferencesor second guess it!!!!...:=

[zepharym]

You can reconstruct the performance data at different weights etc using a drag polar derived from their own performance data...its not hard ...

The max range power was the only thing that doesnt match up ...

[zepharym]

Have no fear....will not be attempting to vary any AFM procedures....just seeking to close gaps in knowledge..its also dangerous using theories that do not apply in practice...im seeking to make theory match practice not vice-versa.

Anyway thanks to all for assistance..
.

[Trematode]

Zeph,

Looking at my BE10 flight manual I think the discrepancy might just be in the chart naming conventions.

At the start of the supplemental performance section for the Raisbeck props, and aft body strakes installed in our King Air 100s there is a note:

"Three levels of cruise performance at 1750 RPM are included: maximum, normal, and long-range cruise."

These three levels coincide with the three sets of charts:

"Maximum Cruise Power"
"Normal Cruise Power"
"Maximum Range Power"

I don't believe the Maximum Range Power chart group will give you the aircraft's actual/theoretical maximum range -- as others have already succinctly defined it.

I believe they've simply given you three sets of power settings to choose from for flight planning purposes. The example they give in our C90 AFM is using max. cruise power charts for the enroute portion, and then the max. range power charts to calculate reserve fuel requirements.

In reality, if winds aren't a factor, it's probably possible to squeeze even more range out of the aircraft by flying at at a speeds closer to what you'd expect: Something between Vmd (Vmd=Max. Glide=135 KIAS in your AFM), and 1.32Vmd as Keith et al. said.