Hello all.

 

As so often happens, while considering V1, VR and V2, I went off on a tangent. Can any of you mathematicians or aerodynamicists tell me whether stall speed is indicated or true in the following expression?

 

V_S = √(2 W) / (r S C_Lmax)

 

 

...

 

It was a late night and my brain gave up its circular path around density, pressure, temperature and elevation. At least rain and ice don't affect the runway friction in FS9. I haven't experimented with different surfaces yet. Weeks of fun ahead of me (to think I paid Captain Sim for this headache...).

 

Finally, I found a lovely graph (x = speed, y = distance) of the pair of curves showing distance to climb to 35 feet and distance to decelerate and stop, with the curves meeting at the critical engine failure speed. A nice illustration of the balanced take-off and the V1 point.

 

 

 

But to the presumed embarrassment of the university in question, they missed out the square root (or the square on the other side) in:

 

"Then, V_lo = 1.2 (2 W) / (rS C_Lmax). "

 

I suppose they meant lift-off, not gear operation.

 

Thanks,

D

Can any of you mathematicians or aerodynamicists tell me whether stall speed is indicated or true in the following expression?

 

I am quite the amateur in this, but I will give it the ol' "educated guess"...

 

ρ is density

 

IAS is just the difference between Dynamic and Static air pressure...

 

Only TAS corrects for temperature (and compressibility)

 

So V should be TAS (in the Lift Equation) and V_s at C_lmax in terms of TAS.

 

"Looking for someone like Col. Scott or Tom (Vicious) to school me" Regards,

 

-Rob

No, the Vs in this equation is actually Equivalent Airspeed (EAS), which at the relatively low speeds and altitudes encountered during takeoff and landing does not require significant compressibility corrections, and is thus functionally equivalent to Calibrated Airspeed (CAS), which in turn is functionally equivalent to Indicated Airspeed (IAS) since we don't simulate calibration errors in FS.

 

EAS (and absent significant corrections, also CAS & IAS) are aerodynamic performance indications. TAS is used for navigation (and navigation-related performance like fuel efficiency and range)--it is not an aerodynamic performance measure per se...TAS is speed obtained from aircraft instrumentation corrected to determine speed in physical space.

Hi Bob.

 

Thanks very much for your explanation.

 

You've simplified my evening considerably-- it's good to know I can use IAS at low speeds, and I suppose airfield elevations generally are relatively low altitude. I confess I'd not encountered EAS before (there's rather eclectic research going on here); I think it will be the tangent of choice this weekend.

 

Best regards,

Dave

Depending on aircraft the indicated airspeed has been corrected for the compressibility error and displays a correct airspeed.

Depending on aircraft the indicated airspeed has been corrected for the compressibility error and displays a correct airspeed.

 

Which ones use EAS? The only one I can think of that uses EAS is the Space Shuttle. Most other expensive aircraft just use CAS.

Which ones use EAS? The only one I can think of that uses EAS is the Space Shuttle. Most other expensive aircraft just use CAS.

 

IIRC the 737 uses the air data computer to correct standard CAS for compressibility. It's been a long time since I've been through that type class.

IIRC the 737 uses the air data computer to correct standard CAS for compressibility. It's been a long time since I've been through that type class.

 

I don't know about that. I've got a 737 manual here with me and it describes the airspeed indicator's pointer and digital counter as "Indicates current calibrated airspeed in knots."

That must have been what I was thinking of. Does it go into detail about out it calibrates the airspeed for different AoAs and flap settings?

No, you'd probably have to look in a maintenance manual for that sort of stuff.

Which ones use EAS? The only one I can think of that uses EAS is the Space Shuttle. Most other expensive aircraft just use CAS.

 

Most jet transport aircraft use Mach number as the primary control and performance parameter in those speed regimes where compressibility error would make for a significant difference between CAS and EAS. The ADC does compensate for compressibility in its internal calculations when computing Mach number--and in an older acft without an ADC (aka a type "A" Mach indicator) compressibility compensation is based on an estimation using altitude. Mach number is a more useful measure of airspeed at high speeds for a number of reasons...but between CAS low/slow and compressibility-compensated Mach number high/fast, the airspeed operating envelope is pretty much covered in most commercial aircraft without need to use EAS.

No, the Vs in this equation is actually Equivalent Airspeed (EAS), which at the relatively low speeds and altitudes encountered during takeoff and landing does not require significant compressibility corrections, and is thus functionally equivalent to Calibrated Airspeed (CAS), which in turn is functionally equivalent to Indicated Airspeed (IAS) since we don't simulate calibration errors in FS.

 

EAS (and absent significant corrections, also CAS & IAS) are aerodynamic performance indications. TAS is used for navigation (and navigation-related performance like fuel efficiency and range)--it is not an aerodynamic performance measure per se...TAS is speed obtained from aircraft instrumentation corrected to determine speed in physical space.

 

V can be either EAS or TAS, it depends on what you enter for the density. If you use standard ISA sea-level density it will be EAS, if you use actual density (based on altitude and temperature, ignoring compressibility) you will get the TAS. During my aerodynamics lectures compressibility was usually ignored up to 100 m/s (about 150-180 knots doing a quick mental calculation).

 

EAS is the airspeed that at sea-level density would provide the same dynamic pressure as a given combination of TAS and actual density.

V can be either EAS or TAS, it depends on what you enter for the density. If you use standard ISA sea-level density it will be EAS, if you use actual density (based on altitude and temperature, ignoring compressibility) you will get the TAS. During my aerodynamics lectures compressibility was usually ignored up to 100 m/s (about 150-180 knots doing a quick mental calculation).

 

EAS is the airspeed that at sea-level density would provide the same dynamic pressure as a given combination of TAS and actual density.

 

Yes, true, and a good point. Airspeed indications used for control/performance by a pilot are, generally speaking, a measure of dynamic pressure as it would be measured at STP. So considering the context of the OP's question (related to performance speeds like V1/V2/Vr/Vlo) the relevant speed would be EAS, and computation must use a fixed rho value of .002377 slugs/ft^3 or 1.2754 kg/m^3 (air density at STP), and not actual air density.

 

IIRC, a practical easy-to-remember rule of thumb for the threshold where compressibility comes into play is ~ 200 knots and 20,000 ft of altitude.

Hello again.

 

Bob and John-Alan, I just returned to ask two further questions only to find you've already answered them. I guess that when flying something like Captain Sim's C-130j in FS9, I can use STP for the calculation and assume the calculated speed will be reasonably close to an IAS, which could then be built into a quick reference table.

 

If I used the table at a high-altitude airport, say La Paz, would I then have to make a correction to the tabulated V_S (or V₁ or V_R) based on the local air density?

 

During my aerodynamics lectures compressibility was usually ignored up to 100 m/s (about 150-180 knots doing a quick mental calculation).

 

So considering the context of the OP's question (related to performance speeds like V1/V2/Vr/Vlo) the relevant speed would be EAS, and computation must use a fixed rho value of .002377 slugs/ft^3 or 1.2754 kg/m^3 (air density at STP), and not actual air density.

 

I think the recreational flying is a long way off yet... lots of data collection to complete. Last night I had a happy couple of hours practising the startup routine and taking off into a couple of dozen stalls while using AFSD to log C_L as an empirical way of determining C_Lmax ; tonight, I think I'll set up a flight for V_S at different altitudes and weights. The flights should confirm the calculation.

 

I suspect there must be a small autism gene somewhere in my heritage.

 

Best regards,

D

 

(sorry- I'm editing this as thoughts occur. I'll leave it alone now)

Instead of messing about further with my last post, I'll explain the direction in which I was heading.

 

My plan was to make a 1-dimensional lookup table for each of V_S, V₁, V_R and V₂ for different aircraft weights. I'm beginning to thing I'll have to expand it into a 2-d matrix to accommodate airfield elevation too, but I'm currently unsure how much of a difference elevation would make. Stall speeds at sea level and at 13 000 feet would surely differ, but would the indicated speeds still be the same. If so, the original table with weight as the only variable would be adequate.

 

I've only tried the test stalls in a narrow range of altitudes so far-- I'll have to experiment.

 

This time it's been a long day behind the soldering iron and I'm yearning for supper and a glass of wine.

 

Cheers,

D