Lowest selectable airspeed or V MIN 2

[silverspeed]

Hello there,

I'm trying to determine how the lowest selectable airspeed or Vmin is derived for an aircraft. So far, my estimation is that this is actually the stall speed plus X knots as a margin of safety added (if any) but what are the variables that govern it. I'd say that the stall speed is a funtion of the aircraft gross weight, OAT, pressure altitude, flap configuration setting, available thrust, possibly even the system setting like PACKS ON/OFF, Bleed air ON/OFF. Any assistance in finding enlightenment, direction, a reference or the answers would be greatly appreciated!

Sincerely,
Silverspeed

 

[davidjh]

Lets start by differentiating between the actual stall speed and the corresponding "certified" stall speed which is used to derive the minimum speeds required for the certification basis. The certified speed will be a conservative speed for any given configuration and flight condition. There are some significant differences in stall speed derivation of a prop vs jet powered airplane.
For a jet, the certified speed is obtained at idle thrust. Higher thrust will drive up the pitch attitude and at some level will result in a lesser weight being supported by the wings with a consequently lower stall speed. This assummes the jet exhaust is not impinging on a lifting surface (as on the C-17), which is a whole different doctoral thesis. On many prop powered airplanes the idle setting actually produces drag, so a setting "up off idle" is determined which produced zero thrust/drag, and it is used in determining the certified speed. Many prop powered airplanes have the prop wash impinging on the wing with resulting large decreases in stall speed as power increases.
Stall speeds do vary as one would expect with "high lift device" setting. On the sophisticated big transports these consist of the leading edge devices, trailing edge flaps and wing speed brake panels. Landing gear position can have an effect, but its usually very small. Anyboby with experience where the gear produced a big effect?
As you state stall speed increases as weight increases, usually in some straightforward relationship. On the big jets you can use the square root of the weight-ratio and be very close.
Center-of-gravity is also a variable. Certified stall speeds are determined at the most conservative CG position. generally this is at the Forward CG limit. The difference can easily be 6 knots from forward limit to aft limit on the big boys. This gets tricky when the forward CG limit is not constant but a function of weight.
Stall speed varys with Mach Number and thus varys with OAT and pressure altitude indirectly. On the smaller airplanes the difference in Mach number from max weight to min weight and from seal level to max certified altitiude is so small that the difference in stall speed can be ignored. On the big boys, with the difference in weight approaching 1/2 million lbs (max takeoff to min flying) and the range of altitudes from -1000ft to the mid 40,000's, the range in Mach number is large and the effect of stall speed substantial. The effect may be limited to the "clean" (ie everything retracted) config, and/or to just the extreme heavy weight regime.
The cert basis used prescribes the minimum ratios above the stall speed which must be used to define the AFM (or pilot handbook/manual) speeds. However, these are just one of the requirements which must be met in defining the minimum operational speeds. Typical other requirements are margin from stall warning onset, margin from natural buffeting (particularly during turns, and (recently) an ability to avoid a stall upon conducting an aggresive slowdown from the stated operational speed. Lastly the manufacturer may have his own requirements, based on his experience.
When the world worked with paper AFMS and Crew-Operating-Manuals these speeds were often simplified so as to provide the crew with rules of thumb (ie; during takeoff climb, flap retract speed is 25 knots above the V2+10 (all-engine climbout speed), and then LE-device-retract-speed is 35 knots above that. Boeing has had a long standing rule of thumb for landing speeds, which I don't recall now. Now with the powerful computers on board the big boys, these speeds are displayed to the crew real time and usually reflect all the nuances.
Hopes this helps.

 

[silverspeed]

Thanks for the excellent response. Would this then be the basis for the best hold speed in a holding pattern? If so, two airspeed designations come to mind with operations in a holding pattern, namely, the minimum fuel speed and the minimum drag speed. Recalling basic flight mechanics, the two are the one and the same, unless each is applied to a different flap conguration as defined in an AFM. I'd be interested to find out what your thoughts are on this. Once again, great job on the info.

Ss

 

[davidjh]

Ss

I'd believe the manufacturer would use min drag speed for holding unless that falls below his criteria for maneuvering margin speed. Again it all changes with the age of the airplane. I'm familar with one jet transport of the late 60s where holding was 1.5Vs. Maufacturer wanted to keep it simple, it provided plenty of margin to stall warning, and the drag curve of the airplane was fairly flat about those Vs ratios so that the fuel flow was "pretty close" to the minimum. The F-100 manual says the manual holding speed is the speed for min fuel flow. The 757 manual says the holding speed provides a 40 deg bank margin to stall warning. I suspect (for the jet transports) that as the computers came on board the manufacturers took the opportunity to fine tune the holding speed. I'd suspect that the maneuvering margins tend to set the speeds. There's been much more attention to these speeds in recent years due to some accidents, usually in icing conditions. I know of one early 1990s airplane where the AP/FMS system will increase the commanded speed as the airplane enters a bank/turn so as to maintain the same maneuvering margin to stall warning. But that allows a slower speed in the "straight's" possibly closer to the exact min drag speed. Hope they believe the autothrottle really is that good at not causing thrust over/undershoots in the roll-in and roll-out portions.

 

[jetmaker]

As a pilot, I was taught that the speed in the holding pattern should be maximum fuel speed (i.e. "endurance") so that one does not waste more than the fuel necessary while in the holding pattern. You really do not care how long it takes to complete a holding pattern, so minimum drag is not important, conserving fuel is. Holds are rarely added into fuel requirements, so each hold starts to eat into the fuel reserve requirements.

Regards,

jetmaker

 

[davidjh]

jetmaker

Perhaps I'm missing a train of thought. Min drag speed should cause min thrust to be used, which should be min fuel flow/used. And as you say that should be "max endurance" (which isn't "max range") since we arn't concerned with going anyplace.

My experience (mostly on the medium to big jet transports)is that the drag vs speed curve is very flat for the "clean" configuration in this speed regime, that manufacturers had some criteria for maneuvering margin, but that now there is more attention paid to the maneuvering margin capability by all involved.

 

[davidjh]

Silverspeed;

Read first 8-9 pages of NTSB accident report AAR-96/01 (its on internet) to get an appreciation of how manufacturers can tend to put pilots into a corner while holding - stall speeds of "fully retracted" wing, max holding speeds of ATC for prop airplanes, and flap placard speeds.