How to calculate top speed of an aircraft

[druine]

I have been trying to figure out (if even possible) how to calculate top speed of an aircraft if I know these:


MTOW weight = W = 220 kg

wing area S = 7.5 m^2

wing profile = Gottingen 533 GOE 533 AIRFOIL (goe533-il) (http://airfoiltools.com/airfoil/details?airfoil=goe533-il)

engine power = P = 20 Kw

propeller efficiency = H (eta) = 0.75

air density = p (rho) =1.056 kg/m^2

I pulled those values "from the hat"

If you are talented with this kind of stuff, could you show me step by step with those values how that kind of calculation should be done.

[Baikonour]

There is a fair bit of info missing to do it accurately, but there are also quite a few empirical 'guesstimates' you should be able to use to give you a ROM estimate.

I'd suggest you pick up a copy of Darrol Stinton's "The design of the Aeroplane" - it's very well presented and will help you answer questions like this one - and of similar ilk.

B.

[Genghis the Engineer]

Our OP needs a fair bit of education to work through stuff like this - you can't really do it by rote.

Anderson's "Introduction to Flight", might be a better primer before progressing to a more advanced text like Stinton.

G

[piperboy84]

Get it in, climb to cruise altitude, firewall the throttle, look at ASI and adjust for temp and pressure. Sorted, anything more complicated than that would nip my hee'd

[India Four Two]

pb84,

My kind of practical pilot! :ok:

[Jan Olieslagers]

At the "practical" smart-asses: just suppose the practice check has already been done, or will be done shortly; and T/S wants to compare the effective max. speed to the theoretical maximum - that would be a good indication of the quality of the design and the build.

Of course it is easier to play the smart-ass than to answer a question as asked.

[piperboy84]

You got me! I admit it, I'm nowhere near smart enough to figure out the aerodynamic calcs. Best leave cracking the enigma of knowing prior to takeoff if I will be flying at 90 or 91.5 Kts to the likes of Orville Olieslagers or Jan Yeager!

Fair play to the OP for trying to figure it out though.

[Genghis the Engineer]

I spent 2 years of maths and physics at school to get into university, then 3 years doing my undergraduate degree in aeronautical engineering - and could work this out. Not from the minimum amount of information provided, but from a more complete data set certainly.

To do so reasonably accurately would take me a while, and if I was preparing for the flight test programme on this little single seater described by the OP I'd do so, of course.

Basically

(1) Estimate the zero lift drag coefficient; I'd do that from ESDA data sheets and a drawing of the aeroplane.

(2) Estimate the oswald span efficiency factor, ditto + aerofoil data. That'll give me Cdi with AoA.

(3) Work out the approximate powerplant propulsive efficiency. I've not done that in 20+ years, but IIRC how to do that is well explained in this book 9780471078852: Introduction to Aircraft Performance, Selection and Design - AbeBooks - Hale, Francis J.: 0471078859 (http://www.abebooks.com/9780471078852/Introduction-Aircraft-Performance-Selection-Design-0471078859/plp)

(4) Work out a drag polar at this mass

(5) Work out a thrust polar at this altitude and full power

(6) Co-incide the two, where the lines cross is Vh, or maximum achievable speed in level flight.


And don't forget to account for CAS/TAS variations with altitude, and engine power with density.


Ultimately however, Piperboy is right - you'll still want to go and fly it and see what really happens, as the above is only an estimate.

But it isn't one of those things that lend itself to a simple prescriptive "here's the order to do the sums".

But, there's nothing wrong with self education. Here's the order I'd go through the books.

http://www.amazon.co.uk/Engineering-Mathematics-K-Stroud/dp/1137031204/ref=sr_1_1?ie=UTF8&qid=1446118992&sr=8-1&keywords=maths+for+engineers

http://www.amazon.co.uk/Introduction-Flight-John-D-Anderson/dp/9814636185/ref=sr_1_1?ie=UTF8&qid=1446119017&sr=8-1&keywords=Anderson+introduction+to+flight

http://www.amazon.co.uk/372/dp/0471078859/ref=sr_1_1?ie=UTF8&qid=1446119078&sr=8-1&keywords=Francis+Hale+performance+selection

Stinton is a superb book (and he was a superb man), but actually if you want an introduction to the very basics of aircraft configuration design, I'd start with this.

http://www.amazon.co.uk/Simplified-Aircraft-Design-Homebuilders-Daniel/dp/0972239707/ref=asap_bc?ie=UTF8

Then progress to Stinton (which I still think is better than Raymer's more advanced books, but Raymer's initial book is a brilliant explanation of the general process).

However, these last two are design books, not necessarily essential for understanding performance of an existing design.


G

[ChickenHouse]

There's a reason planes POH are done by experiments ...

I would take the old fashioned pre-flight thumb and the result is always 42 knots.

[Flyingmac]

It's all here. Simple really. http://naca.central.cranfield.ac.uk/reports/1933/naca-report-408.pdf

[olasek]

how to calculate top speed of an aircraft if I know these:
Clearly these are not enough. The most obvious missing item is some drag value, something that will account for the shape of the fuselage/empannage, in other words aerodynamic properties of the airplane as a whole. MTOW and wing profile aren't enough.

[Capn Bug Smasher]

This here (http://nptel.ac.in/courses/101106041/) will do it for you druine.

In Appendix A - 2 Lecture 36 are example calculations for the maximum speed of a PA-28.

You'll need a bigger hat though, you haven't got enough data right now!

[Pace]

Clearly these are not enough. The most obvious missing item is some drag value, something that will account for the shape of the fuselage/empannage, in other words aerodynamic properties of the airplane as a whole. MTOW and wing profile aren't enough.

I am not a mathematician but there are so many variables its is surely a fairly pointless exercise and one which even the manufacturers get wrong.
i am thinking of the original claims of the diamond twin Star which were way off the claimed performance.

Even two PA28s will be different as power and drag are so variable. How good is the engine, the prop? Is the aircraft rigged the same? are there bugs or dirt on the airframe? are there dents on the airframe and a whole lot of other factors?

Pilot technique? Trimming onto the step?

weather conditions, temperature altitude etc

what are you trying too achieve?

Pace

[Above The Clouds]

89.955 kts

[n5296s]

It's all here. Simple really. http://naca.central.cranfield.ac.uk/...report-408.pdf
Piece of cake then really. Can't imagine why anyone would make such a fuss about it. I mean, what are a few fourth-order differential equations in 8 variables? These experimentalists just can't be bothered with a bit of simple math.

For my part, I'm with piperboy. Of course if you want to make a plane go as fast as you can, you make the cross-sectional area small, reduce the drag coefficient, and all that stuff, but you still won't know how fast it will REALLY go until you jump in and fly it.

[Pilot DAR]

but you still won't know how fast it will REALLY go until you jump in and fly it.

Or, for the greater of my experience, you don't how slowly it actually goes, until you jump in and fly it!

A retired friend of mine was the lead aerodynamicist for deHavilland Canada. He told me that they had calculated the cruise speeds for the Dash 8-100 to within 2 knots, before it ever flew (and their speeds actually were within the 2 knots). But there was a lot of brain power being applied to that....

[Pace]

PD

And the marketing department usually get involved in the calculations :ok: the claimed figures on the original Diamond twin Star were a joke

Pace

[porterhouse]

Even two PA28s will be different as power and drag are so variable. How good is the engine, the prop?
You missed the intention of the original question. We are talking about idealized scenario where all components are brand new, where aircraft has no bugs, no dirt, where engine parameters are well known, etc. Clearly he is not going to get it from this limited and insufficient list of parameters but it can be done, Boeing, Airbus and other developers can pre-calculate aircraft critical (critical for marketing) parameters (like speed, range) with 1% accuracy, this sort of accuracy is expected in some branches of aviation. It takes a lot more effort than throwing some numbers into a mathematical formula but it can be done.

[abgd]

I wonder whether it's easier to predict the parameters for a jet than a propeller driven aircraft. I can imagine that the airflow might be a lot more straightforward in the former.

[Genghis the Engineer]

It is.

In aircraft performance terms, you model a jet engine as producing thrust, whilst a piston engine produces power - which then goes through a propeller which has speed dependent efficiency.

If you really want a headache with the maths, try modelling a turboprop - it's both at once.

G

[Pace]

Surely when a large aircraft manufacturer works out premeditated and forecast performance they use more than just mathematical equations?
I am far from an expert on this so on my part its guesswork but they have access to wind tunnels where they can test and modify structures which make up the aircraft?
Take winglets which may be used on a progressive design?
they will be designed, tested and modified to create an effect?
They will be tested alone in the wind tunnel with sensitive instruments measuring everything from pressure to airflow and then tested with the wing?
That data will then be used to workout performance gains.
I am sure its not a case of sitting down with a blank sheet and saying x+y-z=127.7 KTS

Pace

[Charles E Taylor]

As well as all the textbooks listed. The John Roncz spreadsheets are a great tool for a first look.

https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&uact=8&ved=0CDcQFjADahUKEwjYwYevpfDIAhXBuBQKHS97AyM&url=https%3A%2F%2Frtfmaero.files.wordpress.com%2F2010%2F10%2 Froncz-spreadsheets-v2-1.xls&usg=AFQjCNH0u9_Yuv0VaUjHlH978_OpjG2vCg

I hope this helps.


Charlie

[Genghis the Engineer]

Surely when a large aircraft manufacturer works out premeditated and forecast performance they use more than just mathematical equations?
I am far from an expert on this so on my part its guesswork but they have access to wind tunnels where they can test and modify structures which make up the aircraft?

Generally it would be done "in silicon" first of all - computer design tools which combine aerodynamic and structural estimation.

The results would then be checked by hand calculation by reference to historical data sheets - such as ESDU.

Then sample critical aircraft structure would be built and tested to destruction, and representative models would be put in the wind tunnel, matched as far as possible to Reynolds number, then scaled to the complete aircraft.

Then it's flight tested, to validate the aerodynamic estimates.

Take winglets which may be used on a progressive design?
they will be designed, tested and modified to create an effect?
They will be tested alone in the wind tunnel with sensitive instruments measuring everything from pressure to airflow and then tested with the wing?

Yes.

The main instrumentation will be forces and moments - but it's common to pressure tap sections of lifting surface to generate pressure distributions. When I worked in the tunnel on what is now Typhoon, we also had moveable control surfaces, and re-tested at lots of control settings, AoA values, and even some Beta variations.

Flow visualisation isn't used that much, but has value in identifying interference drag issues, and boundary layer thicknesses for instrument positioning particularly.

That data will then be used to workout performance gains.
I am sure its not a case of sitting down with a blank sheet and saying x+y-z=127.7 KTS

The equations are vitally important, and any performance engineer lives and breathes them. But they require historical and wind tunnel data as part of the inputs to make them really trustworthy. You can't work from theory alone - but also you can't go from wind tunnel results to a full scale aeroplane without a pretty solid set of flight mechanics formulae to work with.

And even then, they're not as trustworthy as flight test data - and there will be differences.

G