Hi everyone,
I'm kinda a newbie to aerodynamics so pardon my questions. I'm trying to do a stability analysis of an aircraft and actually, i'm struggling with stability derivatives:
1- Is CL_alpha the slope of the CL depending of alpha graph ? I thought it is, but actually the software is giving me CL_alpha = 8.1786 and it's not at all the slope of the graph, where did i miss ? (Attached screenshots gives every information needed about graphs and values).
2- How do i collect initial stability derivatives (Like CL_0, CD_0, Cm_0 ...) and drag derivatives in general ?
3- How about forces and moments equations ? For example, i have Cx_u = -0.12005. I wanted to verify the value of X_u (software gives me X_u = -2.8827). But when calculating, it doesnt fit:
X_u = 0.5 * rho * V^2 * S * Cx_u
X_u = 0.5 * 1.225 * 17.57^2 * 2.253 * (-0.12005) = -51.1414
Same with other values, this was just an example. Where did i miss ?
Figures below show details about the stability analysis i designed. Ask me if you need more informations.
I made a mistake in my answer to the first question, see my next post.
Originial answer:
(1. CLalpha is the gradient of the lift coefficient, but the angle of attack is measured in radians.)
2 . XFLR5 gives you the coefficients at the steady state trim condition Cm = 0.
3 . The non-dimensionalisation of stability derivatives is not "standardised" and depends on the author of the underlying equations. In this case you want to have a look at Etkin & Reid, that'll give you the answers you need. Depending on what equations you're working with you need to convert them. CXu != CXu and Xu != Xu in that case!
Cheers,
Stefan
Last edit: Stefan 2024-09-23
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Hi Stefan,
Thank you for taking time to answer me. It helped me but i am still struggling:
1- You are absolutely right, i completely forgot to turn degree into radians, my bad. But even after that, the calculated gradient is about CL_alpha = 6.11 , it's still far from the 8.17 given by XFLR5. Is that normal ?
2- I know, but i'm searching for the initial coefficient values. I thought that, for example, CL_0 is equal to CL_alpha when alpha is null. But since the lift depends on the elevator deflection too, i don't think that it is that simple.
I noticed that CL_deltaE (lift coefficient depending on elevator deflexion) is missing, how can i calculate it ? And how about drag coefficients (CD_0, CD_alpha, CD_deltaE), how to calculate these values since XFLR5 doesn't (i need it in my linearized model) ?
3- I didn't know that equations were not standardised. Thanks for that information !
Last edit: Mahi 2024-09-23
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I just realised that you're speaking about the CLa in the stability derivatives and not "in general". In that case it is NOT the gradient of the lift coefficient as you'd normally assume it to be. Also note that Etkin & Reid use alpha for the non-dimensional derivatives depending on the vertical velocity w, since alpha ≈ w/u_0.
Sorry for the mistake in my earlier answer! But this also illustrates quite well what I meant when I said they are not standardised.
I am not quite sure what you mean by initial coefficients in that case. For me the meaning would be lift, drag and moment coefficent at the trim point (steady state flight) if we're staying in flight mechanics. These are the values XFLR5 gives in the 3D view.
Or do you simply mean the coefficients to calculate the lift, drag and moment. As in CL = CL_0 + CL_alpha * alpha? (In this case CL_alpha of course denotes the lift coefficient gradient)
Cheers,
Stefan
Last edit: Stefan 2024-09-23
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2- Exactly, i'm talking about the coefficients to calculate the lift, drag and moment. My equations are as:
CL = CL_0 + CL_alpha * alpha + CL_q * q + CL_deltaE * deltaE
(Same with drag and moment)
So i started to use XFLR5 to get these values. But actually it doesn't give CL_0 and CL_DeltaE (and none of CD values at all). That's what i'm asking for.
Last edit: Mahi 2024-09-24
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Okay, if you're simplifying the equations that much the approach is of course different from the "normal" stability derivatives, and you don't need the stability analysis in XFLR5 to get the parameters you're looking for.
You can read CL_0 from a normal T1 or T2 analysis as CL_0 = CL(alpha = 0).
As established in the earlier answers, CL_alpha is then of course the gradient of the lift coefficient, which you can simply calculate with any two points from the T1 or T2 analysis.
CL_q might be a bit more tricky. The only idea I have right now would be to roughly estimate what additional angle of attack gets induced through q and then use that factor in combination with CL_alpha to get CL_q.
Since this is already vastly simplified, you can probably get away with only doing that for the horizontal tail and its influence on the moment coefficient.
You can get CL_deltaE with a second (and maybe a couple more) analysis by deflecting the elevator and looking at the difference in CL between the two analyses for the same angle of attack. Dividing that by the difference in deflection angle gives you the coefficient. CL_deltaE = (CL(alpha1, deltaE2) - CL(alpha1, deltaE1))/(deltaE2 - deltaE1)
Cheers,
Stefan
Last edit: Stefan 2024-09-24
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The approach for CD is of course similar. You just need to separate into induced and parasitic (in XFLR5 viscous) drag.
Getting Cm should be analogue to CL.
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Hi everyone,
I'm kinda a newbie to aerodynamics so pardon my questions. I'm trying to do a stability analysis of an aircraft and actually, i'm struggling with stability derivatives:
1- Is CL_alpha the slope of the CL depending of alpha graph ? I thought it is, but actually the software is giving me CL_alpha = 8.1786 and it's not at all the slope of the graph, where did i miss ? (Attached screenshots gives every information needed about graphs and values).
2- How do i collect initial stability derivatives (Like CL_0, CD_0, Cm_0 ...) and drag derivatives in general ?
3- How about forces and moments equations ? For example, i have Cx_u = -0.12005. I wanted to verify the value of X_u (software gives me X_u = -2.8827). But when calculating, it doesnt fit:
X_u = 0.5 * rho * V^2 * S * Cx_u
X_u = 0.5 * 1.225 * 17.57^2 * 2.253 * (-0.12005) = -51.1414
Same with other values, this was just an example. Where did i miss ?
Figures below show details about the stability analysis i designed. Ask me if you need more informations.
Thanks in advance,
Last edit: Mahi 2024-09-20
Hi Mahi,
I made a mistake in my answer to the first question, see my next post.
Originial answer:
(1. CLalpha is the gradient of the lift coefficient, but the angle of attack is measured in radians.)
2 . XFLR5 gives you the coefficients at the steady state trim condition Cm = 0.
3 . The non-dimensionalisation of stability derivatives is not "standardised" and depends on the author of the underlying equations. In this case you want to have a look at Etkin & Reid, that'll give you the answers you need. Depending on what equations you're working with you need to convert them. CXu != CXu and Xu != Xu in that case!
Cheers,
Stefan
Last edit: Stefan 2024-09-23
Hi Stefan,
Thank you for taking time to answer me. It helped me but i am still struggling:
1- You are absolutely right, i completely forgot to turn degree into radians, my bad. But even after that, the calculated gradient is about CL_alpha = 6.11 , it's still far from the 8.17 given by XFLR5. Is that normal ?
2- I know, but i'm searching for the initial coefficient values. I thought that, for example, CL_0 is equal to CL_alpha when alpha is null. But since the lift depends on the elevator deflection too, i don't think that it is that simple.
I noticed that CL_deltaE (lift coefficient depending on elevator deflexion) is missing, how can i calculate it ? And how about drag coefficients (CD_0, CD_alpha, CD_deltaE), how to calculate these values since XFLR5 doesn't (i need it in my linearized model) ?
3- I didn't know that equations were not standardised. Thanks for that information !
Last edit: Mahi 2024-09-23
I just realised that you're speaking about the CLa in the stability derivatives and not "in general". In that case it is NOT the gradient of the lift coefficient as you'd normally assume it to be. Also note that Etkin & Reid use alpha for the non-dimensional derivatives depending on the vertical velocity w, since alpha ≈ w/u_0.
Sorry for the mistake in my earlier answer! But this also illustrates quite well what I meant when I said they are not standardised.
I am not quite sure what you mean by initial coefficients in that case. For me the meaning would be lift, drag and moment coefficent at the trim point (steady state flight) if we're staying in flight mechanics. These are the values XFLR5 gives in the 3D view.
Or do you simply mean the coefficients to calculate the lift, drag and moment. As in CL = CL_0 + CL_alpha * alpha? (In this case CL_alpha of course denotes the lift coefficient gradient)
Cheers,
Stefan
Last edit: Stefan 2024-09-23
1- Understood, thanks !
2- Exactly, i'm talking about the coefficients to calculate the lift, drag and moment. My equations are as:
CL = CL_0 + CL_alpha * alpha + CL_q * q + CL_deltaE * deltaE
(Same with drag and moment)
So i started to use XFLR5 to get these values. But actually it doesn't give CL_0 and CL_DeltaE (and none of CD values at all). That's what i'm asking for.
Last edit: Mahi 2024-09-24
Okay, if you're simplifying the equations that much the approach is of course different from the "normal" stability derivatives, and you don't need the stability analysis in XFLR5 to get the parameters you're looking for.
You can read CL_0 from a normal T1 or T2 analysis as CL_0 = CL(alpha = 0).
As established in the earlier answers, CL_alpha is then of course the gradient of the lift coefficient, which you can simply calculate with any two points from the T1 or T2 analysis.
CL_q might be a bit more tricky. The only idea I have right now would be to roughly estimate what additional angle of attack gets induced through q and then use that factor in combination with CL_alpha to get CL_q.
Since this is already vastly simplified, you can probably get away with only doing that for the horizontal tail and its influence on the moment coefficient.
You can get CL_deltaE with a second (and maybe a couple more) analysis by deflecting the elevator and looking at the difference in CL between the two analyses for the same angle of attack. Dividing that by the difference in deflection angle gives you the coefficient. CL_deltaE = (CL(alpha1, deltaE2) - CL(alpha1, deltaE1))/(deltaE2 - deltaE1)
Cheers,
Stefan
Last edit: Stefan 2024-09-24
The approach for CD is of course similar. You just need to separate into induced and parasitic (in XFLR5 viscous) drag.
Getting Cm should be analogue to CL.
Probably a dumb question: What is a T1 / T2 analysis ?
T1 / T2 refers to the analysis type.
T1 is fixed speed, T2 is fixed lift.
Opposed to the stability analysis, which is T7.
Last edit: Stefan 2024-09-25