r1830

I was trying to figure out why Vmo lowers as altitude increases. This is what I have com up with. Am I on the right track? Thanks

Vmo is a speed defined by the flight envelope which is based on Load Factor and Gust Factor.
Flying above this speed and encountering a gust or increasing load factor may result in structural damage. Airspeed is presented to pilots as indicated airspeed.

In my research, it seems that Vmo/Mmo is based on a Percentage of Mach Speed.
In the limitations section of the BE1900D Manual the Airspeed Limitations Chart lists Vmo from 13,200 ft to 25,000 ft as 248-195 kts indicated airspeed. It has an asterisk next to it that says these speeds correspond to .48 Mach. This implies that the limitation is based on percent of mach speed. .48 Mach would result in an airspeed based on true airspeed and not indicated airspeed. It appears the limit airspeed is based on a true airspeed. As a result, as we increase altitude the indicated airspeed for Vmo will decrease. This makes sense for aircraft that operate at speeds approaching Mach 1. At speeds below Mach 1, airflow around curved surfaces of the aircraft could accelerate to speeds at or above mach 1 which could result in shockwaves forming in undesirable locations and affecting controllability of the aircraft.

Other limit V Speeds such as Vle (landing gear extended) and Vlo (landing gear operating) do not change with altitude. They are not based on true airspeed; instead they are based off of indicated airspeed. Indicated airspeed is essentially a measurement of the volume of air passing a point in a given amount of time. A wing needs the same “volume” of air to pass over/under it to produce a given amount of lift. As altitude increases, the density of air decreases and the aircraft has to fly at a higher true airspeed to maintain that volume of air. Vle and Vlo speeds most often are predicated on the operation of the gear doors. Some aircraft like the 747 have very large gear doors that open up for extension and/or retraction, but then close once the gear cycle is complete. In these cases Vlo will be a lower speed than Vle. Another factor for Vlo might be the amount of stress created on the downlock mechanism. As airspeed increases, parasite drag increases resulting in a greater airload on the landing gear. This load is based on a volume of air passing by, that is why these airspeeds are an indicated airspeed.

ryan1234

I was always under the impression that Vmo was a function of EAS.

JobHopper

First of all, Mach is already a percentage, the ratio of the speed of sound to your current speed at a given altitude. Limiting speeds are not based on a percentage of a percentage.

Second, V speeds do not change with altitude until you hit the limiting Mach speed, at whch time the Mach limit takes over. If you are looking at a chart where the Vmo is decreasing with altitude, then at some point on that graph you passed Mmo and you are actually reading Vmo base on the limiting Mach. .48 M is apparently that speed for the Beech you mentioned.

Dr. Mach discovered that air behaves the same way for a given percentage of the speed of sound, regardless of altitude. That discovery is why he got the speed named after him. Those same laws apply to all aircraft, not just high performance ones. A C-172 would have a limiting Mach if it had an engne powerful enough to go that fast.

ryan1234

It was my understanding, correct me if I'm wrong, but max operating V-speeds have to do with high-dynamic pressure problems, like flutter, aileron reversal, divergence, etc.....as such they are a function of EAS - depending on the effect.

Because EAS decreases with altitude for a given mach number, sonic flow starts to predominate (so Mmo takes over) - because higher altitudes will have lower dynamic pressures (which makes Vmo less critical). In the end, like you said, Mach is a the ratio of true airspeed / speed of sound at that particular temperature.

ZnCrO4

I agree with your first comment, though I believe the second one is more aircraft based. Some aircraft do in fact have a Vmo that will decrease with alt although it decreases at a slower rate as to become higher than Mmo at some transition alt. For instance in the HS125 I believe the Vmo to Mmo is somewhere in the neighborhood of fl330 depending on the day. Vmo starts to decrease above 12k if i remember right. The reason for this I am not entirely certain although I think it may have to do with flutter.

thats all I have to add...

JobHopper

Thanks for the correction. I think like a pilot and not an engineer.

I agree that high speed = high dynamic pressures and EAS measures that speed. How those pressures affect an individual airframe is the reason we have wind tunnels and aero engineers to figure out the limits.

UAL T38 Phlyer

Ryan:

EAS is usually so similar to CAS or IAS that it isn't worth mentioning. V-speeds have to do with dynamic pressure, as you stated.

r1830:

The speed of sound in any gas depends on one thing only: Temperature. The colder it gets, the slower the speed of sound.

Two things happen as you climb: temperature goes down, so the actual Mach-1 speed of sound goes down.

Second: since air density goes down, your Indicated speed starts to be significantly less than your True Air speed through that medium.

So as you climb, at lower indicated speeds, your true speed through the medium is a bigger percentage (Mach nnumber) of a speed of sound that has decreased with altitude.

And the critical Mach of an airfoil (wing or prop) cares only about the ratio of true speed and actual speed of sound.

JobHopper

I think we are all talking the same language. Airflow around an airplane is not a constant; it varies with location. For example, the tip of a propeller could theoretically go supersonic while the prop near the spinner was still subsonic because the tip is moving a lot faster, even though it is the same airplane moving through the same airmass (don't know if that is actually possible, it is just the simplest example I can think of).

So, as you climb, the pressures created by your EAS/Mach vary from wing root to wing tip, from the nose to the tail, etc. A decreasing Vmo as you climb prior to reaching Mmo is probably being dictated by the Mach effects on some part of the airplane, but it is being presented to the pilot as an airspeed.

r1830

Thanks to all for your replies. It is starting to make a little more sense. I really tried to do some research on this subject, but have had a little difficulty in putting it all together. Here is another attempt.

Vmo is a speed defined by the flight envelope which is based on Load Factor and Gust Factor and the effects of airspeed on the aircraft and control surfaces (for example flutter, and the region of reverse command). The top and bottom portions of the flight envelope have limits based on load factor and gust factors. The far right edge of the envelope is based on an airspeed at which adverse handling characteristics such as buffeting, flutter and reverse command on control surfaces could be catastrophic.

I did some computations and think I have a better understanding. For example, Vmo for the Beech 1900D is 248 knots from Sea Level to 13,200 feet. It then decreases from 248 knots to 195 knots (.48 Mach) from 13,200 ft to 25,000 ft. Below are some hypothetical scenarios. For example in the summer at sea level in Alaska on a standard day at 15 degrees and the winter it could be -30 C at the surface. While in a desert area it might be +38C. Some numbers might be a knot or two off as I used an actual E6B for True Airspeed Calculations and I don't have a calibrated airspeed. But I think the results are close enough to help me understand the principle.

Conditions: Sea Level, +15C, 29.92, IAS 248 kts
Mach 1= (Square Root of 15C +273) multiplied by 39 = 661.8 knots
Mach .48 = 317 knots
TAS = 248 knots
So IAS and True Airspeed are equal and less than Mach .48

Conditions: Sea Level, +38C, 29.92, IAS 248 kts
Mach 1= (Square Root of 15C +273) multiplied by 39 = 687.7 knots
Mach .48 = 330 knots
TAS = 259 knots
So IAS is less than True Airspeed and both are less than Mach .48

Conditions: Sea Level -30C, 29.92, IAS 248 kts
Mach 1= Square Root of (-30C +273) multiplied by 39 = 607.9 knots
Mach .48 = 291 knots
TAS = 228 knots
So IAS is less than True Airspeed and both are less than Mach .48

Conditions: 13,200 ft, -11C, 29.92, IAS 248
Mach 1 = Square Root of (-11C +273) multiplied by 39 = 631.2 kts
Mach .48 = 303 knots
TAS = 304 Knots
So IAS is less than True Airspeed
Mach .48 and True Airspeed are approximately equal

Conditions: 25,000 ft, -35C, 29.92, IAS 195 kts
Mach 1= Square Root of (-40C +273) multiplied by 39 = 595.3 knots
Mach .48 = 285 knots
TAS = 291 kts
So IAS is less than True Airspeed
Mach .48 and True Airspeed are approximately equal

Conditions: 25,000 ft, -20C, 29.92, IAS 195 kts
Mach 1= Square Root of (-20C +273) multiplied by 39 = 620.3 knots
Mach .48 = 297 knots
TAS = 300 kts
So IAS is less than True Airspeed
Mach .48 and True Airspeed are approximately equal

Conditions: 25,000 ft, -55C, 29.92, IAS 195 kts
Mach 1= Square Root of (-55C +273) multiplied by 39 = 575.8 knots
Mach .48 = 276 knots
TAS = 280 kts
So IAS is less than True Airspeed
Mach .48 and True Airspeed are approximately equal

In conclusion, Mach Speed is related to temperature. IAS decreases with an increase in altitude. At Sea Level the aircrafts TAS is well below the Mach .48 limit but still has a limit of 248kts IAS. The true airspeed is getting faster as we gain altitude for a given IAS of 248 kts. As we increase altitude, the margin between aircraft's TAS and Mach .48 get closer together. At a certain altitude these airspeeds meet and Mach.48 becomes the limiting airspeed.

UAL T38 Phlyer

Grade: A+

Here's an extreme example:

I used to do functional check flights on F-4 Phantoms. I've been at FL500, indicating 230 knots, and the Mach was 1.10.

Which would mean for your 1900, with a Mach-crit of 0.48, your limiting IAS would be about 110 kts (if you could get a 1900 to FL500)