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Thread: Vertical stabilizer efficiency

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    Registered User Matt G.'s Avatar
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    Vertical stabilizer efficiency

    When calculating rudder control power using the equation (from Perkins and Hage)

    Cr = -av(τ)(Sv/Sw)(lv/b)ηv

    Where av is the vertical tail lift curve slope, τ is the rudder effectiveness parameter, Sv and Sw are the vertical tail area and wing area, respectively, lv is the longitudinal distance from the CG to the VT aerodynamic center, b is the wingspan, and ηv is the vertical tail efficiency, how does one determine ηv? I have an equation for the horizontal tail efficiency, but I'm not sure that applies to vertical tails as well. Unless I overlooked something, no book I own (Perkins and Hage, Raymer, McCormick, or Pamadi) mentions how to determine the vertical tail efficiency. In an example in my college stability and control class notes, 0.9 was used for the Navion example that were were doing. I am going to tentatively use that value for my scale T-28 until I can be steered in the right direction, since the Navion's overall configuration is pretty similar to a T-28. Any thoughts?

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    Super Moderator orion's Avatar
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    Re: Vertical stabilizer efficiency

    As in the calculation for static stability, this efficiency term is for the "quality" of the air that is flowing by. And you're right, I don't recall seeing it specifically defined anywhere either, nor have I seen any hard numbers - just guidelines (which didn't have any references associated with them). The only consistent "estimate" I've seen regarding the value for the vertical tail is that in most instances it is lower than the value used for the horizontal due to blanketing effects of the fuselage, especially at higher angles of attack. Since you're most concerned with the vertical tail at low speed, the effect of the body would be more pronounced due to the inherently higher aoa (versus that for level cruise flight). As a general ballpark, I use 90% of the value used for the horizontal.
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    Re: Vertical stabilizer efficiency

    I would imagine that you would need to account for the rudder floating co efficient if talking about directional stability --we assume no 'feet free' condition if the rudder drive is irreversible or powered or even if aerodynamically balanced but none of this might apply to your 80% scale T28 -- to reduce the trail of the rudder you could use an anti servo tab or increase the horn balance (both of which wouldn't affect the "T 28 like" vertical tail profile --tail shape is pretty characteristic for a lot of aircraft and how much could you alter it in any event without looking wrong ? or lengthening the fuse or both ? Maybe you could get more control power by increasing the rudder chord or double hinging if you suspect it might be inadequate -- aerodynamically rebalancing the rudder or splades or something would add a bit more complexity . Wouldn't the worst case be for a windmilling prop and lower q at the tail (as per Orion's note about the quality of flow ) -- Maybe Stinton has something to say about it -I'll look . (this is related to my thread question about the derivation of vertical tail volume co efficient and Norman posted a very useful rework of that from Mark Drela )

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    Registered User Matt G.'s Avatar
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    Re: Vertical stabilizer efficiency

    Orion-

    Thanks!

    Aircar-

    I have accounted for that...it doesn't appear to be much of a concern. Directional stability coefficient is 0.00353/deg. The control power seems more than adequate (-0.0024/deg) and the maximum sideslip angle that can be corrected with rudder deflection is about 13.5 degrees. Correct me if I'm wrong, but there appears to be a strong relation between hinge line positioning and control force; it seems the more overhang there is, the lower the control forces. Now I think I know why the hinge line is so far aft on the T-28. According to my calculations, at about 130mph, the pedal force is at the FAR23 limit of 150lbf. I guess that makes sense- in my flight experience in a small number of aircraft, rudder control takes more effort than the elevator or ailerons.

    I need to start a thread to post scans of smart-@$$ comments scrawled in the margins by the original owner (circa 1949) of my copy of Perkins and Hage. Some of them are pretty funny...

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    Registered User fly2kads's Avatar
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    Re: Vertical stabilizer efficiency

    Quote Originally Posted by Matt G. View Post
    I guess that makes sense- in my flight experience in a small number of aircraft, rudder control takes more effort than the elevator or ailerons.
    You may already know this, but there was a WW-II era survey that NACA did of test pilots. Their findings were that the test pilots found controls to be "well balanced" when the rudder/elevator/aileron forces were in a ratio of 4:2:1.

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    Registered User 4trade's Avatar
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    Re: Vertical stabilizer efficiency

    Quote Originally Posted by fly2kads View Post
    You may already know this, but there was a WW-II era survey that NACA did of test pilots. Their findings were that the test pilots found controls to be "well balanced" when the rudder/elevator/aileron forces were in a ratio of 4:2:1.
    Very interesting ratios. It might be how our muscle works, like leg is strong compare arm and pulling/pushing is easier than movement sideways. I wonder how is our personal ratios for these...
    Mantra´s like: " it is too difficult" or "it is impossible" is true only for those people who use it...

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    Re: Vertical stabilizer efficiency

    Quote Originally Posted by Matt G. View Post
    When calculating rudder control power using the equation (from Perkins and Hage)

    Cr = -av(τ)(Sv/Sw)(lv/b)ηv

    Where av is the vertical tail lift curve slope, τ is the rudder effectiveness parameter, Sv and Sw are the vertical tail area and wing area, respectively, lv is the longitudinal distance from the CG to the VT aerodynamic center, b is the wingspan, and ηv is the vertical tail efficiency, how does one determine ηv?
    Corke mentions a few values in chapter 6.2.4 (Cvt), being 0.95 for a T-tail, 0.5 for a H-tail and 1 for a V-tail
    Kennis vermenigvuldig je door het te delen.
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    Re: Vertical stabilizer efficiency

    I made change to rudder to get it stiffer at the feel after test pilot comment. I bet 4:2:1 is correct.

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    Registered User Matt G.'s Avatar
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    Re: Vertical stabilizer efficiency

    Aircar-

    Your comment made me wonder if my spreadsheet was correct, as the 'free-rudder' change in stability was extremely low. It turns out I had an error in my spreadsheet. Now that I have corrected that, I have so much control power that there isn't much directional stability left. My rudder-free directional stability is 0.0003/deg; a 'nominal' value from my notes is 0.00175. The rudder-fixed directional stability is 0.00353/deg. Additionally, I'm not accounting for the presence of the dorsal fin, or portion of the rudder that extends below the fuselage center line. I'm not sure how to account for them and what effects they'll have. I've reduced the area of the rudder and reduced the overhang, but that didn't really do anything other than greatly reduce the pedal force.

    I understand how the anti-servo tab works, and it sounds like that would help, as it would increase the pedal force and also lower the amount of stability lost due to 'free-rudder'. I'm not quite sure how to do the calculations for an anti-servo tab though, as all of my books only discuss trim tabs. It might even be that the real T-28 uses an anti-servo tab, as in this picture I took at an airshow last spring, the linkage rod for the rudder tab is at an angle such that it can't possibly be passing through the hinge line, so it can't be a trim tab. I wish I had taken more pictures...all of these little details didn't jump out at me before. I'll probably have to wait until July to see some at Oshkosh this year.
    Vertical stabilizer efficiency-100_7943-custom-.jpg
    So to recap, if I use the existing hinge line, rudder area, overhang, etc. as scaled from the drawing, I have nearly nil free-rudder directional stability (0.00034 /deg), really high control power (-0.0021 /deg), really low pedal force (75lbf to counteract a 15-degree sideslip at 260 ft/sec airspeed) but high pedal force gradients (about 50lbf/degree of sideslip at 260 ft/sec). If I reduce the size of the rudder by about 30% and lessen the overhang, rudder-free directional stability and control power are essentially unchanged, but pedal force becomes even lower, and the pedal force gradients also decrease in magnitude. I'm not sure where to go from here. Ideally I think I'd want to see rudder-free directional stability increase, pedal force increase, leave the vertical stabilizer shape unchanged, and not change the rudder proportions too much. I'm not sure if that combination is even possible to achieve.

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    Registered User Matt G.'s Avatar
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    Re: Vertical stabilizer efficiency

    Ok, disregard most of my previous post...I found another error in my spreadsheet. When I copied the section on hinge moment coefficients from the longitudinal control section of my spreadsheet, I didn't fix the formulas in the cells to reflect the new locations of the values they were using. I think I have that cleared up now. Pedal force is still pretty low, though, so I'd like to get a bit more information on the anti-servo tab

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    Re: Vertical stabilizer efficiency

    Quote Originally Posted by Matt G. View Post
    When calculating rudder control power using the equation (from Perkins and Hage)

    Cr = -av(τ)(Sv/Sw)(lv/b)ηv

    Where av is the vertical tail lift curve slope, τ is the rudder effectiveness parameter, Sv and Sw are the vertical tail area and wing area, respectively, lv is the longitudinal distance from the CG to the VT aerodynamic center, b is the wingspan, and ηv is the vertical tail efficiency, how does one determine ηv? I have an equation for the horizontal tail efficiency, but I'm not sure that applies to vertical tails as well. Unless I overlooked something, no book I own (Perkins and Hage, Raymer, McCormick, or Pamadi) mentions how to determine the vertical tail efficiency. In an example in my college stability and control class notes, 0.9 was used for the Navion example that were were doing. I am going to tentatively use that value for my scale T-28 until I can be steered in the right direction, since the Navion's overall configuration is pretty similar to a T-28. Any thoughts?
    After Orion comment did I fully understand what this was all about.

    Sometimes intuition can be right. I happened to give shape to the fuselage and place the rudder in my diminutive design in such manner that I can claim 95% rudder efficiency of this sep up I have !

    God I love this site !

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    Re: Vertical stabilizer efficiency

    This is a term that is generally found through experimentation rather than calculation. There are "trend numbers" which have been listed above. If you want an actual equation, you can derive η_v from DATCOM's estimation of the combined sidewash and tail efficiency equation as follows:

    Click image for larger version

Name:	tail efficiency.jpg
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    S = Wing Area
    Sv = Vertical Tail Area
    zw = the distance parallel to the z axis from the wing root quarter chord to the fuselage centerline
    d = the max fuselage depth
    ARw = the aspect ratio of the wing
    Λc/4w = sweep of the wing quarter chord
    dσ/dβ = rate of change of side wash with respect to side slip angle
    Warning: My posts occasionally contain strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for adults), and advanced mathematics (which may be unsuitable for liberal-arts majors).

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    Re: Vertical stabilizer efficiency

    GARRRRK! --you win the equation to end all equations contest "garand" ! --strikes me there are a few empirical factors in there still though eg "0.724 +.." - I daren't ask where that comes from and at the further risk of falling into a bottomless chasm "Is that power on or power off ?" (hope you are a monty Python fan and recall the question about the speed that a swallow flies --and the question in return "Indian or English?" ..)

    nV must itself then be applied to get the effective vertical tail volume coefficient (which incorporates the wingspan and other factors not appearing in this ) --I can't believe that the nV term is a constant but must itself must be a variable which includes the q at the tail and a power term to account for slipstream velocity although the d sidewash/dside slip term might be the bit that does some of that it least .

    I just yesterday found Darron Stinton's tome on "flying qualities etc " (follow ups to his anatomy of the aeroplane and design of the aeroplane )in the nearby uni library but didn;t have enough time to pore over it on the nVt question.

    Only from reading I gather that with overhung hinge lines there needs to be an internal seal so that the positive pressure developed on the "inside' of the deflected surface acts both on the part of the rudder ahead of the hinge line but ALSO the extended internal flange along the chord line which is mainly what balances the surface areodynamically (we seal glider control surfaces to stop flow through but with such small chords the hinge moments are miniscule anyway and if there is any pressure involved on the rolling seals it would possibly increase control friction --teflon tape is the usual material used so maybe this is to reduce the friction if the internal tapes do 'inflate') I built a new rudder and fin and stretched the fuselage by 800mm on the Cobra aviation Cobra a few years ago and fitted an "S" seal but didn't know how it flies as that aircraft was not finished for a few years but has flown since (see Cobra aviation website if interested but take it all with a big grain of salt )

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    Re: Vertical stabilizer efficiency

    Website for the Cobra -http://www.tomair.com.au --it was cloned off the Alvarez Poliwagen which was originally a T tail and accordingly had a very thick fin profile and the airfoil section was very poor as 'modified' by the manufacturer . it was vague in directional stiffness as orginally configured the "XLT" refers to eXtra Long Tail I gather ...

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    Re: Vertical stabilizer efficiency

    It is an empirical equation. It is a "force fit" equation that took trend data from many "real world" airplanes and derived an equation that matched the trend line. Alot of "funky" preliminary design equations were created this way. Another that comes to mind that gets screwy if you get too far "out there" is the Oswald efficiency factor. At high aspect ratios (like sailplanes) the efficiency from the equation goes down, but in reality these aircraft have an efficiency around .95 . I recall alot of equations having notes saying "not valid for cases over XXX". I would assume that this equation would only be valid for "normal" airplanes. When in doubt, use conservative values. As others have mentioned, the general practice is to use a generalized number based on the tail configuration. But since you wanted an equation, I figured I would share the one I know.
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