V-Speeds and weight

[shdw]

I am holding a private pilot ground that landed here last week, I refused to give an answer about each speed till next class because I want to be sure I get this right. This is mostly off the top of my head so my apologies if they are off.

As weight goes up:

Best angle of climb goes up because the change in induced drag explained below under best glide would result in the minimum drag being at a higher speed.

Best rate of climb goes down because power required goes up leaving the speed at which the maximum excess power is developed being slightly lower speed.

Best glide goes up because drag goes up because we fly at a higher AOA for the same speed which is graphically shown by the induced drag curve sliding to the right on the graph.

Stall speeds both go up because the speed required to attain sufficient lift to balance weight will need to be higher for the given critical AOA.

Va changes with weight was discussed so I won't bring it back up here, it was discussed here: VA Changes with Weight for those curious.

Min sink goes up with weight because the minimum power required will occur at a slightly faster speed.

Rotate speed will go up for the same given angle of climb departure because speed will have to go up for the same given angle to be able to overcome the heavier weight. In this case I would be assuming 2 of the same aircraft departing both only allowed to use 10 degrees nose up at different weights just for ease of explanation.

Flaps, gear speeds, never exceed and normal operating will not change.



How did I do and what did I miss?

Thanks for the help.

 

[tgrayson]

Best angle of climb goes up because the change in induced drag explained below under best glide would result in the minimum drag being at a higher speed.

Agreed. Alternatively, min drag happens at a particular AoA, and with greater weight, that AoA occurs at a higher velocity.

Best rate of climb goes down because power required goes up leaving the speed at which the maximum excess power is developed being slightly lower speed.

Disagree. Given that Vmin power = .76 * Vmin drag, they must move in the same direction. The mere fact that power required goes up isn't enough to change Vy, because that just changes the quantity of excess power, not the speed at which it occurs. Changing the value of Vy requires moving the point of minimum power, which requires a change in shape of the power required curve. Since the power required curve is derived from the drag curve, its shape reflects change in induced drag in a similar, but distorted, fashion as the drag curve.

Best glide goes up because drag goes up because we fly at a higher AOA for the same speed which is graphically shown by the induced drag curve sliding to the right on the graph.

Agreed.

Stall speeds both go up because the speed required to attain sufficient lift to balance weight will need to be higher for the given critical AOA.

Agreed.

Min sink goes up with weight because the minimum power required will occur at a slightly faster speed.

Agreed.

Rotate speed will go up for the same given angle of climb departure because speed will have to go up for the same given angle to be able to overcome the heavier weight.

Agreed, although I don't see that climb angle is pertinent. I don't see a connection between the pitch angle at rotation vs climb out.

Flaps, gear speeds, never exceed and normal operating will not change.

Partial agreement. Vno has some relation to an aircraft's ability to withstand gusts of certain velocities at cruise speed without exceeding airframe limits, so weight would have some bearing in a similar fashion with Va.

 

[shdw]

Agreed. Alternatively, min drag happens at a particular AoA, and with greater weight, that AoA occurs at a higher velocity.

Interesting way to look at it with the AOA, I like that thanks.

Disagree. Given that Vmin power = .76 * Vmin drag, they must move in the same direction. The mere fact that power required goes up isn't enough to change Vy, because that just changes the quantity of excess power, not the speed at which it occurs. Changing the value of Vy requires moving the point of minimum power, which requires a change in shape of the power required curve. Since the power required curve is derived from the drag curve, its shape reflects change in induced drag in a similar, but distorted, fashion as the drag curve.

Sorry but I can't seem to figure out from this what you are disagreeing with, the reason, the explanation, or both. Will you elaborate a little more on this?

Agreed, although I don't see that climb angle is pertinent. I don't see a connection between the pitch angle at rotation vs climb out.

The angle was only to show 2 situations where everything remains constant (in the lift formula) except total lift must be greater which is accomplished by icreasing speed. So climb angle I guess would be better to say the assumed departure AOA of I don't know, 8 degrees or whatever.

Partial agreement. Vno has some relation to an aircraft's ability to withstand gusts of certain velocities at cruise speed without exceeding airframe limits, so weight would have some bearing in a similar fashion with Va.

I figure it is safer for them not to know that. I rather limitations that don't have different markings for weights (like Va) to be left alone at the private level. But yes I agree they certainly change with weight.

 

[Cessnaflyer]

I love aerodynamics. Thanks for the posts guys!

 

[tgrayson]

Sorry but I can't seem to figure out from this what you are disagreeing with, the reason, the explanation, or both. Will you elaborate a little more on this?

You said that Vy would go down, when it actually would go up, for much the same reason that Vx goes up. The power required curve is simply the drag curve multiplied by the velocity.

Alternatively, minimum power, like minimum drag, occurs at a particular AoA, and the airspeed at which that occurs goes up with weight.

 

[shdw]

You said that Vy would go down, when it actually would go up, for much the same reason that Vx goes up. The power required curve is simply the drag curve multiplied by the velocity.

Alternatively, minimum power, like minimum drag, occurs at a particular AoA, and the airspeed at which that occurs goes up with weight.

Uh oh, I disagree because everything I have read about climbs (Edit: removed "including POH..." I was thinking of something different here) and what I was taught was rate goes down angle goes up until they meet at absolute ceiling. You can see it pretty easily by drawing 2 Pa/Pr curves and this is how it was shown to me. The power required curve moves up and to the right as weight increases which leaves the gap for greatest extra power available sitting at a lower speed than it does at the original start position. However at the same time the curve moved forward so Vx went up.

If your going to prove this wrong do you mind digging into some more detail here or just further explain what you have already? I planned on doing that graphical representation I just explained above for 2 different weights and showing the gap change of Vy down and the bottom of Pr now being higher for the higher Vx.

 

[tgrayson]

The power required curve moves up and to the right as weight increases which leaves the gap for greatest extra power available sitting at a lower speed than it does at the original start position.

Whether that happens or not depends on the shape of the power available curve. The classic respresentation of the Pa curve for a constant speed prop is a relatively flat line. Assuming it to be completely flat for simplicity, Vy would be solely determined by the move of minimum power to the right.

The merging of Vx and Vy is something normally associated with an increase in altitude. I do agree that there would be a similar effect with an increase in weight. There is no need for Vy to ever decrease in order for that to happen; all that's necessary is that Vx increase at a greater rate than Vy.

 

[shdw]

Whether that happens or not depends on the shape of the power available curve. The classic respresentation of the Pa curve for a constant speed prop is a relatively flat line. Assuming it to be completely flat for simplicity, Vy would be solely determined by the move of minimum power to the right.

The merging of Vx and Vy is something normally associated with an increase in altitude. I do agree that there would be as similar effect with an increase in weight. There is no need for Vy to ever decrease in order for that to happen; all that's necessary is that Vx increase at a greater rate than Vy.

I noticed my association with this in the POH before that I had edited out. I see what you mean I have two similar things correlated that shouldn't be. Screw Jepesen books cause thats where I read it most recently which probably made me think about all this crap.

If I am getting this right, a constant speed prop there would be little to no change in Vy because of the near flat power available curve. On the other hand with a slightly curved power available on a fixed pitch there may be a slight decrease in Vy?

Furthermore I think it might be important to note that in high performance pistons/turbos and into jets Vy certainly goes up with weight. Now that you mentioned the power available curve which I know is flat on higher performance and jets. As weight increase the power required curve would shift right and the Vy would go up with it. Meaning Vx and Vy would be effected equally as long as the aircraft had a power source that produced a relatively flat power available curve.

I think this link shows what you are talking about with a high efficiency prop: http://home.scarlet.be/comicstrip/EnginePropeller Eff_files/acprop.gif


Hopefully I have this right now?


PS: Obviously for my private pilot class I wouldn't go into all this detail.

 

[tgrayson]

If I am getting this right, a constant speed prop there would be little to no change in Vy because of the near flat power available curve. On the other hand with a slightly curved power available on a fixed pitch there may be a slight decrease in Vy?

Are you talking with altitude? If so, yes. I show the diagrams on my web site. The decrease in Vy with altitude is due to shifts in the power available curve. The power required curve, when plotted in indicated airspeeds, merely increases with altitude, it doesn't change shape (when plotted in TAS, as is normally the case, it rises and rotates). In reality, the Pa curve for a constant speed prop isn't perfectly flat, hence you will normally see *some* change in Vy with altitude.

 

[shdw]

Are you talking with altitude? If so, yes. I show the diagrams on my web site. The decrease in Vy with altitude is due to shifts in the power available curve. The power required curve, when plotted in indicated airspeeds, merely increases with altitude, it doesn't change shape (when plotted in TAS, as is normally the case, it rises and rotates). In reality, the Pa curve for a constant speed prop isn't perfectly flat, hence you will normally see *some* change in Vy with altitude.

My entire post was in reference to weight. The first paragraph was trying to explain that I had in properly associated the Vy changes with weight with the Vy changes in altitude. The second 2 paragraphs are in regards to Vy and weight.

Basically for small pistons/fixed prop Vy will decrease slightly with weight increase but constant speed props and jets with relatively flat power available curves will see an increase in Vy. The fixed pitch prop has a curved power available curve so when power required shifts up and right with a weight increase the position of Vy falls at a slightly slower airspeed.

Sorry about the confusion with altitude before, ignore everything with altitude now I meant to only speak of changes from weight, that is what the posts about. Thanks again for helping me out.

 

[tgrayson]

The fixed pitch prop has a curved power available curve so when power required shifts up and right with a weight increase the position of Vy falls at a slightly slower airspeed.

I used the flat power available curve just to simplify the mental imagery. I can't construct a Pa curve that supports the idea of Vy decreasing with an increase in weight.

I just created a spreadsheet with parabolic Pa and Pr curves, and shifted the Pr curve up and to the right several times with varying parameters; the velocity of maximum power increased each time.

 

[shdw]

I used the flat power available curve just to simplify the mental imagery. I can't construct a Pa curve that supports the idea of Vy decreasing with an increase in weight.

I just created a spreadsheet with parabolic Pa and Pr curves, and shifted the Pr curve up and to the right several times with varying parameters; the velocity of maximum power increased each time.

Would you mind telling me how you did that? I imagine just numbers in a graphing calculator, but what numbers. I want to show this to my students then because if I am going to disagree with the book I would like to be able to prove it.

Thanks and obviously this being true I agree with you.

 

[tgrayson]

Would you mind telling me how you did that?

I'll send you the spreadsheet if you want. It's really just simple parabolic curves (i.e., X^2), one of them inverted. The power required curve is actually cubic, but I don't think that's critical to getting the general flavor of how the numbers move. You can shift the curve up or down by changing the intercept, and then left or right by adding or subtracting a number from the independent variable. I visually inspected the excess power column to view how it moved.

 

[shdw]

I'll send you the spreadsheet if you want. It's really just simple parabolic curves (i.e., X^2), one of them inverted. The power required curve is actually cubic, but I don't think that's critical to getting the general flavor of how the numbers move. You can shift the curve up or down by changing the intercept, and then left or right by adding or subtracting a number from the independent variable. I visually inspected the excess power column to view how it moved.

That would be great, and yes I am sure I will smack myself when I see the sheets. But I can't think of how to "measure the difference" or give the power required curve its shape, we did it in class 5 years ago. I forgot that long ago so sure if you want just private message me or post them here for everyone to look at.

 

[tgrayson]

I am sure I will smack myself when I see the sheets. But I can't think of how to "measure the difference"

Yes, you will. I "subtracted" the power required from the power available to get the excess.

Remember, I wasn't trying to make real power curves; I do have formulas that would allow me to construct more realistic curves, but I was only after the general shape. Plotting speeds of -30 to 30 and plugging them into an X^2 formula was enough to provide the general shape over the curves. A -X^2 inverts it.

I used the Open Office spreadsheet, which is a clone of Excel. Here it is:

pa.ods

If you don't have Open Office, I also saved it out as an Excel 2000 spreadsheet, but I can't promise as to its compatibility:

pa.xls

 

[shdw]

Great graph, thanks. I put it up in Excel and playing with the movement up the X/Y axis to show forward and upward movement from the increase in weight still giving a higher X value on the graph. Hopefully I can explain this now when I try to teach it to these people.