# Flight physics for a roll [closed]

I am working on a pet project to write a game with flight physics. It will not be a simulator but instead much simpler.

What I have done so far

I have created winged components that generate lift and drag using the basic formulas I found online. I apologize if some of the debug info is not standard terminology.

The green arrows in the image show the force and magnitude begin applied. The yellow lines are the relative airflow.

What I cannot get working and understand

At first all the components used the same forward speed calculated by looking at the CG. Just an easy way to see what speed the plane was moving. The plane flew straight when "thrown" level and if will self correct if thrown with a slight roll angle.

The problem starts when each component starts calculating its individual forward speed. Even with dihedral applied to wings the plane will start rolling to the left more and more.

You can see that the left wing has a slightly higher AOA as the result of the dihedral. BUT it has a lower velocity than the right wing because the plane is yawing (I think). This lower velocity causes the right wing to produce more lift and the plane rolls more to the left. The more it rolls left the more the right wing speeds up causing it to produce even more lift.

I have tired to increase the rudder, but that didnt help at all. Removing the rudder causes the plane to over correct, and then to roll to the left too.

Can any body explain what is suppose to happen when a plane rolls. From what I see the plane rolls left, it pitches slightly down. The right wing "swings" forward faster than the left causing more lift.....

• It's not completely clear if you are trying to model an intentional pilot-commanded roll -- like a complete aileron roll? -- or how the plane reacts if a bit of turbulence puts it into an unwanted bank angle the pilot does nothing to correct. In the latter case it's not really a "roll" that you are trying to model-- I'm trying to think what would be a clearer terminology-- – quiet flyer Oct 27 '18 at 17:43
• I apologize, i see what you mean. This is without any pilot input at all at this stage. Its basically a model plane begin "thrown" and it was not completely level at that moment . There is no turbulence or any forces acting on the plane except lift, gravity and drag. Imagine one of those 2 part balsa planes where you slide the wing into a slot in the body. You throw it, but the wings are at a 45' angle. The plane starts leveling out right after you launched it. My question is why does it level out, I am not seeing that in my model as the outside wing generates more lift. – Charl Cillie Oct 27 '18 at 21:58
• The problem I was facing is known as Spiral Stability and it seems the dihedral and rudder surface area play the biggest rolls. rc-soar.com/tech/spiral.htm – Charl Cillie Nov 26 '18 at 16:09

Typical airplane is not stable in roll. The outside wing flies a bit faster, which does indeed make it produce a bit more lift and that in turn will make it bank into the turn, tightening it and if left uncorrected, ending in a spiral dive.

In a coordinated turn, an aircraft even can't be made stable in roll. There is no way to create a restoring force without involving side-slip. The only thing that can be provides is the yaw-roll coupling where a slip produced a rolling moment into the slipping turn. This rolling moment is affected by dihedral and sweep.

Fortunately as the turn tightens, if the rudder is held fixed, some slip does develop that can provide the restoring force reducing the bank. However, it causes another dynamic mode, the Dutch roll.

As the bank increases, the tendency changes from Dutch roll to spiral mode. If you wanted to avoid the spiral mode, the Dutch roll would be very strong, so practical aircraft are designed with moderate yaw-roll coupling and do require a bit of opposite aileron in turns.

• I see exactly what you described. The plane at the moment does continue into a spiral dive. My only flying (I have done myself), has been with model airplanes. I was expecting it to behave in the same manner. If you look at a typical "first RC plane" like a Gentle Lady Gilder that does not have ailerons, but only rudder and elevator controls, what causes this model to self correct on a roll ? Lets say you aggressively used the rudder that caused the plane to yaw and roll and you center the rudder again. Why would that not also continue into a spiral roll ? – Charl Cillie Oct 27 '18 at 21:49
• @CharlCillie, it probably has quite strong yaw-roll coupling. Still I would think it would continue in a spiral dive if you made a sufficiently sharp turn and only centered the rudder instead of using opposite input to end the turn. – Jan Hudec Oct 27 '18 at 22:01
• "In a coordinated turn, an aircraft even can't be made stable in roll. There is no way to create a restoring force without involving side-slip " -- this is an important statement for all amateur enthusiasts of stability and control dynamics to understand. – quiet flyer Oct 28 '18 at 0:30

Your question is challenging to understand quickly, let alone answer well. For starters, what exactly are you doing with dihedral? Do you understand how the roll torque created by dihedral, in any given situation, is entirely due to sideslip, and the resulting way that the sideways airflow "sees" each wing at a different angle-of-attack?

If not, that's one thing that would need to be fixed before you can continue with this. If you want your "model" plane to automatically tend to slowly roll back toward level in the absence of aileron deflection, you are going to have to model how banked, turning flight involves a curving flight path, which means that there is a curving aspect to the relative wind, which tends to make the vertical fin "feel" a sideways airflow, which generates a yaw torque that displaces the nose toward the outside of the turn, exposing the wing to a sideways airflow. Like this: https://www.av8n.com/how/htm/yaw.html#sec-long-tail-slip . It's not sufficient to imagine that the plane just tends to "fall" toward the low wingtip whenever it banks-- that's not really what drives the slip. It's all about the curving flow. And it's certainly not correct to imagine that the dihedral (or the high wing placement) will create ANY self-leveling tendency at all, in the absence of slip (sideways flow).

So basically there's so much going on here that you may need to ask about ten different questions to even start to "unpack" how your computer model needs to be improved. A good start would be to peruse this website and play close attention to all sections that deal with yaw stability, roll stability, sideslip, roll control, etc -- https://www.av8n.com/how/

It's normal for an aircraft with only modest dihedral to tend to wind up into a steeper bank angle, but if you aren't accurately modeling the stabilizing effects of dihedral, as I'm guessing may be the case, you'll end up over-estimating this tendency for the bank angle to increase on it's own.

I'd encourage you to try to think of some more narrow, individual questions to ask to help you "unpack" your problem some more.

• Imagine if you can the days before remote controls where "toy" planes would only have a motor that would pull it up into the air in a slow spiral. No pilot input. The motor would run out of fuel and the model would glide down. I expected dihedral would be the main reason for the plane not to roll over. I do see that the the lower wing has a bigger AOA and it makes sense. The problem is that the upper wing has a higher air flow speed, causing it to have more lift. Instead of correcting the plane it rolls it more. I am trying to understand why the real world one does not roll over too. – Charl Cillie Oct 27 '18 at 22:05
• Thank you for your reply and links. They are a pot of gold to me. I will work on exactly on what I am trying to find out and after going reading all the info you linked to, get back. – Charl Cillie Oct 27 '18 at 22:12
• It's true what you say about the higher wing, the wing on the outside of the turn, having a higher airspeed. It's also true what you say about the lower wing having a higher angle-of-attack due to to dihedral, in the presence of a sideways flow toward the high wingtip, but the question of exactly what is causing the sideways flow is not a simple one. It's not really adequate to imagine that the aircraft is simply "falling":toward the low wingtip. Anyway, I see that you are on the right track in some ways in terms of trying to think critically about some of these issues. – quiet flyer Oct 28 '18 at 1:03
• Thank you for taking the time to share your knowledge. I am going to dig in and find why I am not seeing the results I expect and share it here. – Charl Cillie Oct 28 '18 at 22:06