How do you measure G?

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Ken Bones
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How do you measure G?

Postby Ken Bones » October 9th, 2012, 7:52 am

Hi all, I am building a 1/4 scale yak 50, it will be approx 92'' span. Now the plan is to throw this thing about quite a bit, but, how do I know if the wing can take it?
So some questions.
How much G would be thought to go accross the wings.
How do you measure the G in the first place during flight.
Would there be more Gs the further you get to the wing tip.
How do you measure how much G the wing can take in the workshop.

Bonzey :?

Andy Boylett
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Re: How do you measure G?

Postby Andy Boylett » October 10th, 2012, 10:40 pm

Ken,
There are a number of commercial g force sensors you can buy now-a-days. They directly measure the g force experienced and can either log it for download when you land or some will transmit it back to a screen as you fly. There are some cheap ones on HobbyKing and better quality ones elsewhere.

You have to remember that g force can be in 3 directions and is dependant on the exact point where you measure it ie. one part of the plane can have high g while another part has not! The g force you are really worried about for the wing structure is the vertical g force (when plane is the right way up) at the centre of the fus ie. the g force perpendicular to the wing spars, measured at the fus centre.

You can calculate the estimated force on the wings with this formula:
Force= (weight of plane x speed squared) divided by the radius of the turn measured about an axis along the wing spar.

So if you can estimate what sort of speed you are going to be doing and how tight a turn you will pull then you can measure the force on the wing spars.

ie. weight = 10kg, speed = 40mph = 16.7 m/s , radius = 10m

Force = 10x16.7**2/10 = 279 Newtons or 28.4 kg (1 kg = 9.81 Newtons)

Cheers, Andy

Ken Bones
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Re: How do you measure G?

Postby Ken Bones » October 11th, 2012, 11:24 am

Thanks Andy.
Now could you supply an idiots guide plz!

Ken.

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Re: How do you measure G?

Postby Mark Partington 2989 » October 11th, 2012, 5:46 pm

Ken, the simplest way of answering your question, (I'm not allowed to comment on anything Andy says), is that;

1. just about all of it
2. you measure 'G' with an accelerometer, (many different one available from places like EagleTree or HobbyKing - and can be accessed by live telemetry of recorded to be downloaded later.)
3. It varies with wing shape, section and washout/in, but for a parallel chord, non-swept, no-washout wing you can say it's roughly mid-span, (washout moves it inboard).
4. If you want to test to the limit, (i.e. destruction), support the wing around mid-span for the full chord, then using the CofG as your 'test point' hang or place weights on the wing at the CG until it breaks. Divide the weight used by the total aircraft weight and the result is the 'G' the wing can support. Take 2/3 of that value and that's your safe 'G' figure. In full size, you do the reverse and balance the wing at it's center and spread the weight along the wing, but you'd need to know where and how much weight to use at each point, but you need to know the exact loading at each point along the wing to do that.

I suggest speaking with Ted Allison, as IIRC he did something similar with his big AT-6, by calculating the loads the wing would be stressed to during flight, and then building the wing to carry those stresses, I'm sure he did the same when he designed his Frightning as well.

Mark.
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Rob Buckley
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Re: How do you measure G?

Postby Rob Buckley » October 11th, 2012, 8:11 pm

In pictures, the 'Load Case 19' at the bottom of the page below gives a fairly good indication of the load testing process.

http://www.sonexaircraft.com/research/updates/onex/onex_update_121010.html

As a rough estimate, the load distribution on the wing will be very similar to the layout of sandbags they use; that is maximum at the wing root, and nothing at the wing tip.

The full size was stressed to +9 / -6 g, although some folk were apparently killed when the wings came off at +12g. Depending on how you're going to fly it, going for the full size limits as a minimum would be a good bet.

If the model weighed, say 9Kg, to survive +9g with a safety factor of 1.5 (to give a bit of margin), you would need to be putting 61kg on each half of the wing in a static load test...
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Andy Boylett
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Re: How do you measure G?

Postby Andy Boylett » October 16th, 2012, 10:31 am

Ken Bones wrote:Thanks Andy.
Now could you supply an idiots guide plz!

Ken.

But that was the easier guide. I have put below this message the full differential calc for centripetal acceleration, although it is 25 years since I last tried to use that :) :) :) :)


The easiest way is just is just to estimate g from your flying style. If you are going to to crazy 3D then anything from 10 to 20g likely.Sedate flying 1 or 2 g. Tight, fast loops, maybe 4 or 5g.

Then use this to give you your wing loading by multiplying your model weight by the g figure.

So your 10kg model at 5g will put 50kg load on the wings.

Regards, Andy


CENTRIPETAL ACCELERATION

In two dimensions the position vector \textbf{r} which has magnitude (length) r and directed at an angle \theta above the x-axis can be expressed in Cartesian coordinates using the unit vectors \hat{x} and y-hat:[10]

\textbf{r} = r \cos(\theta) \hat{x} + r \sin(\theta) \hat{y}.

Assume uniform circular motion, which requires three things.

The object moves only on a circle.
The radius of the circle r does not change in time.
The object moves with constant angular velocity \omega around the circle. Therefore \theta = \omega t where t is time.

Now find the velocity \textbf{v} and acceleration \textbf{a} of the motion by taking derivatives of position with respect to time.

\textbf{r} = r \cos(\omega t) \hat{x} + r \sin(\omega t) \hat{y}

\dot{\textbf{r}} = \textbf{v} = - r \omega \sin(\omega t) \hat{x} + r \omega \cos(\omega t) \hat{y}
\ddot{\textbf{r}} = \textbf{a} = - r \omega^2 \cos(\omega t) \hat{x} - r \omega^2 \sin(\omega t) \hat{y}

\textbf{a} = - \omega^2 (r \cos(\omega t) \hat{x} + r \sin(\omega t) \hat{y})

Notice that the term in parenthesis is the original expression of \textbf{r} in Cartesian coordinates. Consequently,

\textbf{a} = - \omega^2 \textbf{r}. ie a =r.w**2

chris willis
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Re: How do you measure G?

Postby chris willis » October 16th, 2012, 2:05 pm

Come on Bones keep up. :D

Tony Collins 1073
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Re: How do you measure G?

Postby Tony Collins 1073 » October 16th, 2012, 3:14 pm

Really glad he didn't give us the hard version :lol:

Ken Bones
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Re: How do you measure G?

Postby Ken Bones » October 16th, 2012, 5:48 pm

It was just a thought! Didnt realise it would be such a long winded awnser.
Wouldnt the G be different though along the wing span?

Bonzey

chris willis
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Re: How do you measure G?

Postby chris willis » October 16th, 2012, 5:55 pm

Use a G string to measure it :lol:

Andy Boylett
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Re: How do you measure G?

Postby Andy Boylett » October 16th, 2012, 5:58 pm

Ken Bones wrote:It was just a thought! Didnt realise it would be such a long winded awnser.
Wouldnt the G be different though along the wing span?

Bonzey

Hi,
The g force is the same all along the wing as this the acceleration of the wing....it all accelerates at the same amount.

The force (or weight) that is felt at the different points along the wing is distriubuted from the wing root to the tip. At the wing root the full force is felt, at the very tip nothing. Rob Buckley mentioned this.

stewart clifford
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Re: How do you measure G?

Postby stewart clifford » October 16th, 2012, 6:20 pm

In short, put a decent spar into your wing, cover it, fly it if it breaks it wasn't strong enough.

Chris Lane
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Re: How do you measure G?

Postby Chris Lane » October 16th, 2012, 6:44 pm

Stressing is easy - you just need to know what the loads are and where they act!

Simon Wright
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Re: How do you measure G?

Postby Simon Wright » October 16th, 2012, 8:30 pm

I think the calculations with turn radii estimate work but how do you control turn radii, and velocity to maintain these estimated G loads. the use of G meters is great but a bit of a bolting the stable door exercise once the model is designed and built.

I view G loading from the other direction, unless you are planning to design the model for a crash or impact load the G load in flight can only be a product of velocity and lift.

in which case the G load is simply a factor of the cl at vmax and the maximum cl obtainable at re equating to vmax. for instance, a model aerofoil may have a maximum cl of 1.0 and a vmax for straight and level flight where lift = drag say 0.1 so max G = 1/0.1= 10 g. the only forces acting on the wing and airframe are thrust, lift drag and weight. That is a maximum worst case scenario where the wing is taken from Vmax to Cl max in an instant witout reducing velocity.

A quick estimate of velocity is to multiply prop pitch in inches by rpm in K so a 55cc motor turning a 10" pitch prop should max out at about 10" x 7k rpm =70mph depending on airframe drag. throw another 10% on for a slippy airframe and take 10 or sooff for a draggy biplane and you have a starting point.

I stressed some carbon spars on a large and slippy glider and the calculated figures were jaw dropping, 20g being the worst case design point.
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Re: How do you measure G?

Postby Simon Wright » October 16th, 2012, 8:40 pm

Ref the loading, Highest stress is at the wing centre, spar strength tapers according to station on wing. The bending moment o the spar is actually split into tension and compression loads in the top and bottom spars with the webbing or infill area coping with the buckling and shear.

You can do all the fancy lift distribution calcs but as always they are based on estimates and fudge factors so whle precise may not be at all accurate. A simple reduction of stress pro rata with span will give you figures within a few percent on either method.

After all this waffle, probably better not to re-invent the wheel, Go out and find a model that has similar size weight and flying performance to your design and copy the spar design that is known to work.

I
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Andy Boylett
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Re: How do you measure G?

Postby Andy Boylett » October 16th, 2012, 9:58 pm

Simon Wright wrote:That is a maximum worst case scenario where the wing is taken from Vmax to Cl max in an instant witout reducing velocity.


Simon, Your whole explanation is very nicely put. The only thing I would add is the non-aerodynamic event that my son conjured up when he snapped the wings off one of our planes.....go high, dive fast, yank plane instantly through 90 degrees, putting the wings flat on to the direction of travel and hence acting as a sail and not an aerodynamic wing. :( I can't remember how you calculate this one.

Simon Wright
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Re: How do you measure G?

Postby Simon Wright » October 16th, 2012, 11:06 pm

Thanks Andy,

When an object is travelling through the air, all we have are aerodynamic forces. Non aerodynamic forces only happen when all the sky is above the model.


A sail ,parachute and even a sheet of paper is a wing of sorts.

I thinnk the example you are quoting is based on the idea that given enough height, in a vertical dive the force of gravity will continue to accelerate the model at 9.81 m/s2 until it reaches terminal velocity. the only problem with this theory is the limited altitude at which we operate and the effects of drag. if you flew at 70 mph (32 m/s) at 200m altitude then applied down elevator to a vertical dive the aircraft wuld theoretically accelerate at 9.81 m/s for just over 3 seconds where it would meet with terra firma at some 250 mph. the effects of drag (and hopefully the pilot with gentle stick input) would slow this terminal figure.

However a short dive can produce overspeeding which due to lift forces would fold the wings. the point of this is that IF we are to design for terminal velocity dives, the model will need to be stressed for 30- 50 or maybe even 100g. building to those sort of G levels will produce a model of such weight that it will never fly making the whole process futile.

An airfoil travelling perpendicular to the airflow will not be creating lift, only drag. if I remember ocorrectly the CD of a flat plate in this orientation is about 2.0. the drag force D = Cd * A * .5 * r * V^2

Another take on this is to ask how the wing manages to get into a position where it is 'flying' perpendicular (AoA >90 degrees?) to the direction of travel. a difficult operation in itself when few airfoils can fly past an aoa of 12 or 13 degrees before stalling. if you manage to pull the aircraft through a quarter loop out of the vertical dive you are now travelling in the classical straight and level sense?

I fly a lot of 3D (after stall) and I think that to do 3D we fly models in clasically stalled conditions by virtue of prop thrust countering weight rather than the wing, prop wash creating false AoA, and conservation of energy. But that is not really the subject originally broached.

Nice discussion BTW ;-)
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Andy Boylett
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Re: How do you measure G?

Postby Andy Boylett » October 17th, 2012, 9:38 am

Thanks Simon. It's 25 years since I did any of those sums and since university I have only really used the structural stuff and not aerodynamics! Your explanations brings back memories of horribly complicated equations :( :( .

I like your idea that to get back to a 'sail' position in a vertical dive really means having to aerodynamically fly into it. This makes a lot of sense. :D

Cheers

Mike Booth
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Re: How do you measure G?

Postby Mike Booth » October 17th, 2012, 9:59 am

Ken a simple static load test as Rob Buckley suggests will suffice .
If only there was any sort of spar designed in the wings!!!!!!!

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Re: How do you measure G?

Postby Mike Booth » October 17th, 2012, 12:36 pm

The thing is all of the above is irrelevant when you consider that we are talking about two pieces of polystyrene .
I personally hate and detest the stuff as it has no properties to offer other than carry an aerofoil shape.
When you add veneer to the polystyrene you have gone some way in a crude sense towards a composite wing as the veneer starts to form a monocoque structure .
The addition of glass cloth and resin add to the torsional strength of the skin considerably.
However the polystyrene still contributes nothing in the way of strength to the overall wing.
You have to establish a vertical bond between the the two skins in the way of a wing spar. Strategically placed ribs in the high load areas around UC points will also disperse loads to the spar and monocoque structure.
My point really is that you could cut out 98% of the foam for all it's worth in terms of strength.
Start with a wing spar and add to that, preferably full span.


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