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Saab 340 Longitudinal Stability

FSMuseum

FSMuseum

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us-kentucky
Hello all,

I am creating a flight model for a Saab 340 using a book on estimation of stability and control derivatives by Dr. Jan Roskam. In that book, he details how to use various coefficients of standard-configuration (tail-aft) aircraft to determine the static margin.

One of those factors is the volume coefficient of the horizontal tail, or:

Sh * lh / Sw * c

Where:
Sh = Horizontal tail area (theoretical, including fuselage area)
lh = Distance from LEMAC to c/4 of horizontal stabilizer
Sw = Wing area (also theoretical)
c = MAC length

By using this formula and creating a 3D model from official measurements and station diagrams from a Saab 340 WBM, I get the following:

Sh ~ 147.025 sq ft
lh ~ 29.6 ft
Sw ~ 450.039 sq ft
c ~ 6.839 ft

Solving the above formula results in a tail volume coefficient of a whopping ~ 1.4! Which is several times larger than I would expect for such an aircraft and as a result, my static margin calculations fall somewhere around 90% which is ridiculous!

I estimate that the proper volume coefficient for an aircraft like the Saab 340 should be around 0.3 or so, but I cannot figure out where I have gone wrong with my math here. I have quintuple-checked my MAC location on my flight model as well as MAC length, overall model proportions, and the CG locations (also directly from the WBM).

Any ideas? I can provide more information on the aircraft if necessary.

Thanks!
 
Your math looks correct, but your estimated value of 0.3 for horizontal tail volume is way too low for this type of airplane. A more typical value for this type would be around 1.0 .
Roy
 
I think you are correct that my estimation is low. Even still, 1.4 seems excessive especially given the high static margin this yields.

Perhaps it is not so surprising though given that my empty CG is well forward at 9% MAC. The designers at Saab apparently designed this aircraft such that the CG will almost always move well aft during loading. I will complete my flight model and report back on how it seems to perform.
 
I finished up the flight model, and it turned out that I was miscalculating my static margin (as well as a small host of other minor problems! :D ). The numbers now make much more sense and my volume coefficient actually worked out to about 1.0, just as Roy said.

It has left me with an interesting question that I couldn't find an adequate answer for: what reference point show my Cma curve in Table 473 follow? Should it be set based on the OEW CG position, a CG at 25%, or some other reference? Setting it by the OEW CG seems the most logical but I'm not certain.
 
Not sure what you mean here. 473 is Aircraft moment Coefficient versus Alpha or Cm alpha. The typical table has alpha in radians from -180 to +180 and CM is symmetrical about alpha=0. That would be for a symmetrical airfoil ie non-cambered. I suppose it would be different for a non-symmetrical airfoil, but I'm not sure where CG comes into play in this table. I think it does not.
Roy
 
Roy Holmes said:
Not sure what you mean here. 473 is Aircraft moment Coefficient versus Alpha or Cm alpha. The typical table has alpha in radians from -180 to +180 and CM is symmetrical about alpha=0. That would be for a symmetrical airfoil ie non-cambered. I suppose it would be different for a non-symmetrical airfoil, but I'm not sure where CG comes into play in this table. I think it does not.
Roy
Click to expand...

I am not referring to the airfoil, but to the aircraft. As the CG moves the linear portion of the slope of table 473 should change to reflect the changing static margin. My question is, what is the reference point for the initial slope? If I set it to the OEW CG of 9%, the slope is significantly steeper than it would be for a CG at 25%.
 
Now I see what you mean. The steeper the slope the greater the stability or the amount of trim needed when speed changes. So it is up to you as a designer to choose. I prefer a shallow slope with only a small trim input required with speed changes.
Roy
 
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