stall speed and altitude

[FOD]

Now I know that stall speed will increase as altitude increase due to the fact that the density of air decrease. However, just got done refreshing up on Vmc stuff and the book says that Vmc drecrease with altitude while THE STALL SPEED REMAINS THE SAME. I completly understand that there is a critcal altitude where the stall speed and Vmc will converge. But don't agree with their explanation that the stall speed stays the same with altitude. Am I crazy or mixed up somewhere?

 

[Minuteman]

Nope, they're right that stall speed shouldn't change with airspeed as long as you're plenty subsonic. Allow me to ramble.

Simply as possible, lift is a function of dynamic pressure (q) and angle of attack (alpha).

An airspeed indicator is really measuring the difference in pressure between ram air and the ambient static pressure. This difference is the dynamic (differential, q) pressure created by moving through an airmass (q = ½rhoV², where rho is ambient density and V is true airspeed).

So say you want to generate some amount of lift to keep the plane flying but want to maintain the same AOA (maybe you're already near the critical AOA). At either sea level or 10,000 feet that leaves you with:
1) a constant lift force
2) a constant AOA

That means you also need a constant q, which is also a constant indicated airspeed, to maintain that lifting force regardless of altitude. Also note that because rho decreases with altitude, V² must increase to keep q constant. In textbooks anyway.

When your airspeed gets above about Mach 0.25 (160kt @ 10kft), compressibility begins to significantly affect the dynamic pressure measurement and the indicated airspeed no longer reflects the same pressure differential the lifting surfaces encounter.

 

[jeskoe]

Nope, they're right that stall speed shouldn't change with airspeed as long as you're plenty subsonic. Allow me to ramble.

Simply as possible, lift is a function of dynamic pressure (q) and angle of attack (alpha).

An airspeed indicator is really measuring the difference in pressure between ram air and the ambient static pressure. This difference is the dynamic (differential, q) pressure created by moving through an airmass (q = ½rhoV², where rho is ambient density and V is true airspeed).

So say you want to generate some amount of lift to keep the plane flying but want to maintain the same AOA (maybe you're already near the critical AOA). At either sea level or 10,000 feet that leaves you with:
1) a constant lift force
2) a constant AOA

That means you also need a constant q, which is also a constant indicated airspeed, to maintain that lifting force regardless of altitude. Also note that because rho decreases with altitude, V² must increase to keep q constant. In textbooks anyway.

When your airspeed gets above about Mach 0.25 (160kt @ 10kft), compressibility begins to significantly affect the dynamic pressure measurement and the indicated airspeed no longer reflects the same pressure differential the lifting surfaces encounter.

I have a headache.

 

[B767Driver]

Now I know that stall speed will increase as altitude increase due to the fact that the density of air decrease. However, just got done refreshing up on Vmc stuff and the book says that Vmc drecrease with altitude while THE STALL SPEED REMAINS THE SAME. I completly understand that there is a critcal altitude where the stall speed and Vmc will converge. But don't agree with their explanation that the stall speed stays the same with altitude. Am I crazy or mixed up somewhere?

I think this is a pretty simple one. The TAS for stall will increase with altitude. The IAS for stall will remain pretty much the same for all altitudes.

So looks like you're both right.

 

[MidlifeFlyer]

Now I know that stall speed will increase as altitude increase due to the fact that the density of air decrease. However, just got done refreshing up on Vmc stuff and the book says that Vmc drecrease with altitude while THE STALL SPEED REMAINS THE SAME. I completely understand that there is a critcal altitude where the stall speed and Vmc will converge. But don't agree with their explanation that the stall speed stays the same with altitude. Am I crazy or mixed up somewhere?

Minuteman gave a good explanation. Here's a really simple summary for jeskoe's headache.

First of all, the book is probably talking IAS or CAS (not TAS) here since the book values for Vs and Vmc are (almost?) always listed in one or both of these speeds, not in TAS.

The starting point is the differebce between CAS/IAS on th eone hand and TAS on the other. Assuming you understand that, let's leave it as IAS/CAS is based on airflow. Likewise stall speed in a given configuration is based on airflow. When the IAS, is say 80, the number of air molecules hitting the pitot and flowing over the wings is the same regardless of altitude. TAS goes up because the airplane has to be going faster through the air to get the same amount of airflow because of the lower air density.

That's why Vs and IAS/CAS speeds based on Vs (based on airflow) remain the same regardless of density altitude. They are a measuer of airflow, not speed through the air.

But Vmc, like Vy, is also base on available power (and prop efficiency). And, as we know, available power diminishs with less air density. That's why their IAS/CAS numbers decrease with altitude.

 

[BobDDuck]

Keep in mind too that when working with VMC it is often simplified to the fact that the stall speed will not change at all with altitude even though it will slightly (as shown in previous posts). The point the are trying to make is that VMC will change much more rapidly then the stall speed will. It is an oversimplification but I have seen a few books that do that. Remember too that even though VMC goes down with altitude due to the loss of thrust generated, the control surfaces become less effective in thinner air, leading to an increase in VMC. However, this decrease in control performance is so much smaller then the decrease in engine performace it doesn't really matter. Clear as mud, right?