Some Forces

[Howard Rush]

I set out to calculate lift and line tension on an airplane doing a regular round loop.  It was more trouble than I figured it would be.  The plot is attached.  It's a 64-oz. airplane flying at constant speed on 70-foot lines, 5.3-second laps.  There is no wind or other forces on the airplane other than line tension, lift, and weight.  I have two questions (other than does this look correct at all):

1. What's a good assumption for worst-reasonable-case slowing down going uphill in a loop?  I could assume constant power, I guess, but I'd need to guess what power is.  I could do that if I had some data on calm-air loop times vs. level flight.  Better would probably be some strobe pictures of an airplane doing a loop. 

2. Would anybody like to look at my spreadsheet to see where the 0.2-lb. error comes from?  I calculated lift, line tension, and drag, then added them back up to see if they summed to the force required to do the loop.  They don't quite add up at the sides of the loop. 

[Tim Wescott]

1: that it will be a subject of arguments for hanger jocks for years to come.  Given all the statements I've heard about the regulating effect of constant speed motors with big props &c., I don't know that constant power, or constant thrust, or constant speed, or anything is a valid assumption.  Swellular phones have movie cameras on them these days -- you should be able to capture a loop then find the center of the blob from frame to frame.

2: All I see is a graph, where are the equations?

[Howard Rush]

All I see is a graph, where are the equations?

On a spreadsheet.  Want it?

[Tim Wescott]

My email address is in my profile.

[Igor Burger]

Not so clean measuring, but can tell something anyway :- ))

I did not fly laps to save logging time, it was 6 years ago, memory was expensive :- )))

[Mark Scarborough]

Howard,
I have an eagle tree data recorder that  you could strap on and fly with if you want some "real world" data,, assuming you had an airplane to fly now,, It has several available data input sources including airspeed.

[Howard Rush]

Thanks, guys.  Igor's data should do it. Looks like insides went from 70 to 90 and outsides from 60-80.  I presume that it's in kilometers per hour, but it probably doesn't matter.   

[Tim Wescott]

Well, I haven't looked at your spreadsheet (bad me), but after spending more time than I should have on trigonometry and less on geometry, I've pretty much proved that if you ignore drag and assume that the aircraft is providing no aerodynamic side-force (i.e., that line tension is purely due to resisting the centripetal effect), then the line tension is the sum of the mass times speed squared divided by radius always, minus the mass times acceleration due to gravity times the sine of the angle above ground.  This is regardless of the radius of the turn that you're executing (although realistically, the tighter the turn the more likely it is that the aircraft will roll and some of the lift will show up as line tension).

Less clear from the analysis that I've done so far, but pretty obvious once you realize that the only thing that lift can do for you when your wings are straight is to accelerate you along the surface of the sphere defined by the lines, is that the lift is the sum of a component that's straight "up" (or "down") on the aircraft and is proportional to speed^2 * radius of turn, plus the cosine of the weight due to gravity times the angle above ground.

This bears out my own observations, namely that on those occasions where the airplane is trimmed to not roll badly, the line tension seems to be primarily a function of aircraft speed and altitude: if I don't let it go too slow, it maintains line tension just fine everywhere, albeit lighter in the overheads; if the engine run is sick or if I'm really slamming it around & making it slow down, then the line tension suffers.  And finally, to prove the importance of making sure that the assumptions are valid, if I don't have the roll trim correct for whatever reason, then the line tension will suffer on those maneuvers where the plane rolls in.  Note that if you're trying to see this yourself you have to be on the ball: the line tension is a function of the square of the speed, and we're not always used to watching for the speed of the plane.

[Brett Buck]

Thanks, guys.  Igor's data should do it. Looks like insides went from 70 to 90 and outsides from 60-80.  I presume that it's in kilometers per hour, but it probably doesn't matter.    

   If you want closer-to-real numbers I am sure that scaling it to whatever your level flight speed is would be good enough. I suspect that it could be either km/hr or feet per second, but since I go about 78 fps, it's close enough.

    The surprising part is that the lowest airspeed is in the wingover, if I read correctly. I hope mine isn't doing that!

     Brett

[Howard Rush]

I scaled it as you said and had it slow down in a cos-1 function so it was slowest at the top.  If it slows down 13%, an RCH more than Igor's did, the change in potential energy can be accounted for by the change in kinetic energy.  I'm not sure what this means, but it seems not to account for the increase in induced drag from .03 lb. in level flight to 2.18 lb. (a delta of .32 HP) at the start of the loop.  Next I might do me some constant-power simulations with different power until I match Igor's minimum speed.   I'd guess that would let speed peter out quicker as it goes uphill.  Or I might give my new airplane a toot of dope so I can fly some stunt someday.   

[Igor Burger]

It is electric model with constant speed governor and 12x6 prop. So Brett if you feel it better with IC, it will be clear if it adds some power upphill (4-2-4), or because the motor has more power (3 blade low pitch prop).

The speed is in km/h.

The lap time was set to rather slow, higher speed will give model little more kinetic energy, so it can keep speed better. (potentional energy from bottom to top of loop is the same, so it slows less from higher speed)

[Howard Rush]

From Igor's current data, I see that it's doing some regulating.  My idea of assuming constant power using Igor's speed decrease probably does not represent reality.

We can see one of Igor's training secrets from his data.  He does the stunt pattern while climbing a hill.  That is what makes him a champion. 

[Igor Burger]

Nooo, I simply fly figures higher and higher, do not you see that I am landing on the same place? 

Hmm ... but seriously, It is probably some thermal drift, or something ... that sensor has enough resolution to show figure sizes, but not so great stability ... at least it shows if it goes up or down

[Howard Rush]

I wasted some more time.  I posted a chart below in pdf and jpg formats.  The pdf is more readable. This is the 64-oz. Impact again.  I don't know how much power it takes for level flight, so I tried three different powers, then showed how speed, lift, and line tension vary while doing a loop at constant power.  This is actual propulsive power delivered to the air.  Divide by prop efficiency (.6, maybe) to get engine power.  I'm using the physics definition of power, not the one stunt fliers use, whatever it means.  Different levels of power imply different levels of airplane drag.  

I added constant-speed plots to show how wonderful the world would be if we could actually fly constant speed.  They are the upper, flatter curves for airspeed, lift, and line tension.  Then, in the second set of charts I plotted the incremental HP (again the actual propulsive power delivered to the air) it would take to hold constant speed.  I think this is quite interesting.  

[Larry Cunningham]

Fascinating discussion and data - I liked being able to look at Igor's data and "seeing" his pattern maneuvers.. And Howard's been rather funky recently.. It's all impressive, I'll be gawking at this stuff and other things you cats are playing with.

Best regards,

L.

"If you don't take your meat, you can't have your pudding!" -Pink Floyd, The Wall