Vmc Versus Weight

[hdaae]

From what I understand Vmc decreases with increase in weight (single engine operation)

Reasons (from what I gather):

Acceleration=Force/Mass

more mass, harder to move (accelerate, change direction)

With the aircraft banked 5 degrees into the operating engine, the weight becomes a component in the horizontal lift, so with increased weight, increased Horizontal comp. lift. which increases control and therefore decreases Vmc.

But, with increased weight we need increased Angle of attack which increases the angle of the decending propellerblade.
This would change the thrustline and in a conventional aircraft with the right engine operating it would seem that increased weight increases the asymetrical thrust....? and therefore increases Vmc...?

If someone could give me a detailed mathematically/physics explaination or give me a link to a webpage that explained it I would be grateful!

['%MAC']

You are correct when you say that weight will act as an horizontal component of lift when banked (Wsin(theta)). This component acts to oppose the turning moment created by the asymmetrical thrust, reducing the rudder pressure required, hence more controllability with the same fin.

You are also correct in your observation that the thrust line will also change with an increase in weight. The P-factor is moving a matter of inches, while the sin(theta) component of the weight easily offsets this change. A change of thrust of 1 foot (from let’s say 8.58 to 9.58) would change the moment by 11%. This change of thrust is rather large, being about ¼ the radius of a typical prop, but let’s suppose. Now a change of weight from 14,000 to 16,000 is a 14% increase. I really can’t imagine the p-factor moving out that far, but alas I have no hard data on the distance that P-factor moves. Guess I really didn’t positively answer your question. But I think the weight increase offsets the p-factor, after all how much is your AoA going to change, 2 or 3 degrees?

[hdaae]

Thanks for the reply!

I concluded the same way you did as far as which factor were the most significant since every publication Ive read states that with weightincrease you get reduction in Vmc.
I still find it puzzeling that noone have taken the time to write a little about the balance between Pfactor and Horizontal component of lift. These are opposing forces as far as influencing Vmc, and anyone that is a little inquizitive will ask this question to their instructor. I did during my MEI, and my MEI didnt know.
My students are now asking me..and I give them my best theory (which is as you explained, but I dont have it in writing)

With no bank into the operative engine and increase in weight, the P factor would actually increase Vmc.
But, then..again...noone has put Acceleration=force/mass into the equation of it all.

I know Im taking this a little far, but I hate leaps of faith when the subject is clearcut physics and maths