basmntdweller

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I was wondering if a maybe 150-175% Tensor for Nitro power would havee similar flight properties. I was thinking of using a Saito 91 for power and building as light as possible, profile fuse and built up stick style surfaces.
Any thoughts George?
Thanks,,,Matt

GRH

Hi Matt,
Yes I think an Tensor that is scaled up properly would have very similar characteristics. I should also say that one might already be in the works so stay tuned. I'd recommend that if you are really interested in scaling a Tensor up that you study how to use scaling laws. I've been using the square-cube scaling laws for years and they are extremely helpful in modeling. There was a nice article in this months Model Aviation on the subject. A good understanding of square-cubed scaling is a must for every modeler interested in increasing or decreasing the size of a design while retaining its flying characteristics.

George

basmntdweller

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I thought that was a very good article on scaling laws! On building a larger profile version, would you make the side force generators with a flat plate, thick airfoil or thin?
Thanks,,, Matt

basmntdweller

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I thought I'd do some planning on building a nitro Tensor. I referred to the MA article and tried some of the scaling formulas. According to the numbers in the article, the Tensor should only weigh 4.9 oz and my nitro powered version with a 48" span should only have an AUW of 32 oz if I am recalling the formula correctly.

Weight in oz= .0001 x span^3.2778

I know better than those numbers. I don't think anyone could build a 48" span biplane with a Saito 91 on it at only 32oz!
I was thinking more along the lines of 5.5-6 lbs ready to fly.

Any thoughts??
Thanks,,,Matt

I'd be happy to hear more info if there is going to be a nitro Tensor released, say 40-60 size. If it's going to happen, I could skip scratching mine and just wait for the kit or ARF which would be preferable as I already have too many projects for this building season!

GRH

Matt,
When using the scaling laws it's best to pick a starting point or a known value. Lets say you have an airplane that weighs 12oz, 350in^2 of wing area and a span of 36"

b1=36in
S1=350in^2
W1=12oz

b2=50"
S2=?
W2=?

Lets say you want to increase the wingspan to 50". What should the new weight and wing area come out to be?

What I do is first obtain a scaling coefficient which in this case will be the ratio of the spans b2/b1

k=b2/b1=1.39

Note that all areas vary with k^2 and all volumes vary with k^3...this concept comes from the square-cube law detailed in the MA article. If you want to know the new wing area, (S2) simply multiply S1*k^2... 350in^2*1.39^2= 675in^2. If you want to know the new weight you multiply W1*k^3 = 12oz*1.39^3 = 2lb.

Now what does this all really mean? It simply means that if you scaled up every particle in the airplane exactly by the scale factor you'd have an airplane that had the wing area and weight predicted by the square-cube law. Scaling laws must be used with care because the principle behind the concept is that you have to use the exact same material (equivalent average density)to construct the model.

Another thing that you'll find is that the square-cube law knows nothing about aerodynamics. In the case of very small (low Reynolds number) lifting surfaces the aerodynamics can't keep up with the square-cube scaling...you find this to be the case if you scale down a giant scale aerobatic model to foamy size. For example:

b1=120"
S1=2500in^2
W1=40lb

scale this down to a 30" span
k=0.25
S2=156
W2=10oz

While this is somewhat close, we know that we can do better and get a foamy with a 30" span to weigh of 6-8oz with 225in^2 of wing area like on the shockflyer.

I hope this helps,

George

BTW I would simply use a flat plate for the SFG's.

Bill Mixon

Interesting topic..

I have put together a few of my own design that are very similar to the tensor. So far all have been in the 26"-32" range. After seeing how well this design flies, I upsized it to 70" span, and have the fuselage done for it so far. I had hoped that I would be flying it by now, but I can not seem to find the time to finish it.
It's basically 70" X 70" which doesn't seem that big, but it's got a LOT of surface area. Aprox 2000 sq." on the wings, almost 1000 sq" on the SFG's.
Power will be electric, Hacker C50 with Lipo so it's going to be a little heavy. I hope I can keep it under 10 lbs. 9.2lbs is my calculated goal, but I always seem to end up with some extra "mystery" weight in the end.

msm9724

Bill post some pics!

Devin McGrath

sounds awsome caint wait to hear the flight report ...^^^^post some pics^^^^

kennyandannie

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Okay Bill,

It's after Christmas, I think we've given you plenty of time.

Post some pics!!!

It sounds very interesting.

Ken

Bill Mixon

OK, OK..
I guess I should have got those before posting. Here you go..

Jleyland

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Awesome Bill! I can't wait to see more pics. I can only imagine how well that'll fly! Great work

kennyandannie

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Pretty sweet Bill,

I take it your going to run the Hacker 90 ESC? You might want to use this instead of the 77.

That and a 8S3P-6000mAh LiPo pack, your going to be set!

Keep us informed, please.

Ken

Bill Mixon

Thanks, Jon.
Thanks, Ken
I'll start a thread on it when I get it done.
I would like to have one of those nice 90-0 ESC's along with a programmer, but at $400+ I just can't see it. I'm using the 77 3p with this motor which is fine as long as it gets the cooling it needs. I'm only running it at 1500 watts or less anyway. The power system is being flown in [link=http://www.rcuniverse.com/forum/fb.asp?m=1243061&key=]this[/link] plane right now. I'm currently using a 5000 7s2p Tanic battery on it with a 22X10 or 22X12 apc prop.

kennyandannie

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Good stuff Bill,

I'll be building one of 3D Foamy's 35% Extra's, and my suggestions are what I am going to be using. I'm very new to large scale electric, so I'm going on recommendations, not experience.

I don't understand all of the logistics yet, but I'm learning.

Thanks for the info,

Ken

GRH

Bill,
That's awesome! Thanks for sharing that with us. Happy Holidays,

George

Bill Mixon

Thanks, George

tmenet

George,

Thanks for pointing out that great article. Check me out to see if I am oversimplifying things here but another question answered by that article in the AMA (at least to me) is why the bigger your plane gets (when made of the same materials) , the slower it "appears" to land. You have to interpret the facts a little but the data is there in a crude way.

The article states that the "minimum speed!" multiplier for doubling a planes size is 1.5. That means that if you double the length, the minimum speed is now only 1.5 times what it used to be. So if your eyes judge speed by fuselage lengths per second ( a reasonable assumption) an airplane that lands at say 6 fuselage lengths per second when small, would land at 4.5 fuse lengths per second when doubled in size.

Ex:

assume the following...

fuse length = 4 ft
landing speed = 24 ft/s
fuse lengths/sec = 24ft/s / 4 = 6

2X scaled plane would be,

fuse length = 2X4ft. = 8 ft
landing speed = 24 ft/s X 1.5 = 36ft/s
fuse lengths/sec = 36 ft/s / 8 = 4.5


Like I said, this may be oversimplifying it a bit, but finally ( for me ) there appears to be a hard reason why big planes just "seem" to land nicer. Of course all this goes out the window when you are talking about going from balsa to foamies. I guess their wing loading can be so much lighter that they escape the illusion of higher stall speeds inherent in small balsa/glow airplanes.

What do you think George? Be easy, I am an electrical engineer.

GRH

Albert,
This scale speed illusion you talk about is the same thing I stumbled onto 12 years ago when I first started playing with square-cube scaling. There's lots of square-cube scaling for electrical stuff too but that's not my cup of tea.


Here's a reprint of another post I made on RCU that addresses your question...notice that going from balsa to foam doesn't matter that much.

Also be careful using that AMA article...the author breaks a serious rule when he starts to interject his observations of weight growing as k**3.2 not k**3...square-cube is a law and should be kept pure in our use...if our building doesn't follow it's prediction it's because we didn't build it properly.

************************************************** ******************************

Scaling laws are really interesting for modelers...it's a part of virtually everything we do. Often it's assumed that we're scaling from a full-scale aircraft but with so many variances in sizes these days we can apply scaling techniques within the confines of the models we fly.

The scaling of any general object must follow the "square-cube" law which defines (using my nomenclature) a change in scale by a change in a characteristic linear dimension.

If L1 is the length of the original object and L2 is the scaled version of that object then the scaling factor k is defined as:

k=L2/L1

You can derive the square-cube law by applying this technique to a simple geometry like a cube. You will see that the surface area of the cube will grow with k^2 and the volume of the cube will grow with k^3 such that:

S2=k^2*S1 (area)
Vol2=k^3*Vol1 (Volume) (mass, weight and force also scale with k^3)

If we apply this to our wing loading problem we start with a particular airplane with some characteristic length (typically the wingspan) which I'll call b. k is set by the ratio of the wingspans

k=b2/b1
likewise the wing area will grow with k^2 and the weight will grow with k^3 such that
S2=k^2*S1
W2=K^3*W1

If we define wing loading as W/S then we have k^3/k^2 = k so we know from the square cube law that :

(W/S)2=k*(W/S)1 This simply means that if you double the scale you can double the wing loading.

The reason for the so-called "cubic" wing loading also comes from the square-cube law. Modelers don't like to have to remember what wing loading is appropriate for their scale model so they find a figure of merit that works for all scales. This happens to be W/S^1.5 If you look at this using what we've already discussed you get that k^3/(k^2)^1.5 = k^3/k^3 = 1 so it's independent of scale.


You can play this game all over the place...for instance take the level flight linear velocity. The standard equation for lift is L=W=CL*q*S=CL*rho/2*V^2*S...assuming that air density and CL are independent of scale (which they aren't exactly...this is where Reynold number, Mach number and Froude number come into play) you find that V is proportional to (W/S)^0.5

Therefore velocity is proportional to k^0.5...this means that if you double the scale of the airplane the level flight speed increases by the square root of 2 or 41%.

Since we actually see scale speed as body lengths per second we can note that the time it takes for us to see the distance of one body length covered is given by

t=BL/V (body-length/velocity) we know that this is k/k^0.5 or k^0.5 so now we can see that

t2=k^0.5*t1 or stated differently, the model that's double in scale will appear to take 41% longer to cover this characteristic length.

This is quite interesting because the true linear velocity of the double-scale airplane is in fact flying 41% faster but appears to fly 41% slower.

You can also use scaling laws on power. If you say that the thrust required for level flight is approximately equal to D and that the power required is Drag*Velocity (D*V) you get the following:

P2=k^3*k^0.5 = k^(7/2) or k^3.5 This means that power required grows at a little faster rate than volume.

You can test this by scaling a 40% airplane down to foamy size. if the 40% has a span of 120" and uses a 16HP motor how much HP would an airplane of 30" require to have similar performance?

k=30/120 = 0.25 P2=0.25^3.5*16HP = 0.125HP or 93 watts (this is close to what we get running 12V at 8 amps.


You'll also notice that things like moments will scale with k^4 and moments of inertia will scale with k^5, RPM will scale as k^0.5 .....on and on.

The one thing to remember is the square cube-law knows nothing about aerodynamics and in many cases the aerodynamics can't keep up at the lower Reynolds numbers...in this case things like wing area have to grow to obtain similar performance.

George Hicks

tmenet

George,

Concerning your reprint of your earlier post....I love it when you get geeky!

Concerning the AMA article, I noticed the k**3.2 point he was trying to make but I think he eventually blamed the trend on noise limits requiring us to put larger engines on the giant scale end turning props slower to meet the noise limits that we impose on ourselves. I am not sure because he somewhat sidestepped the issue for a while. But I didn't think to deviate from the theoretical k**3 as a design goal for similar performance after reading his article.

About going from balsa to foam... So what the heck is it that makes foamies like your Ultimate feel like they are floating effortlessly and land so slow like the big planes? Is it the flat wings? I have flown .20 cu in balsa/glow planes that were versions of .40 and .60 and the smaller they were, the quicker they seemed to land??? Foamies seem to reverse this trend.

I simply thought that the foam profile construction you used allowed you to get lower wing loading than traditional balsa building techniques letting you beat the t=BL/V (body-length/velocity) illusion???

GRH

Albert,
You like geeky huh? I would keep that to myself bro.

I had to dig through the pile of clutter and find this issue again...I'd completely dismissed it once I saw his weight trend.

The author makes the statement at the top of page 44 that, "The trend equation indicates that span and weight are not related by the cube power, but but 3.22. This is 9 times for a model of twice the size_not 8. Could this be another factor in the scaling law?".

FWIW, his trend is a collection of 9 data points (models) that are hardly a good sampling. Not that the square-cube law is up for alteration by any sampling...I for one don't want the 1)Todd Long Tiny, 2)Mountain Models Tantrum, 3)Gary Wright E3D, 4) Magic ARF, 5) Excite, 6) Eclipse, 7) Lanier Edge 540T, 8) H9 Extra 300L, 9) Lanier 40% Staduacher to collectively set the weight trend for all of model aviation.

Imagine if I decided that because I measure 9 forces and found that they were equal to mass*acceleration^1.05. You wouldn't stop using f=ma.

In other words all I'm really saying is that W2 not equal to k**3.22*W1. Unfortunately this 3.22 permeates the entire article from there on out. His parameter list is tainted by this from weight on. Here's what the list in table 2 on page 46 should read.

weight ~ k**3 not k**3.22
W/S ~k not k**1.22
minimum/max speed ~ k**0.5 not k**0.61
kinetic energy at min speed ~don't really know why this is in there but it should be k**4 not k**4.4
Power Required ~k**3.5 not k**3.8

Another point is that the argument that noise limits cause this k**3.22 trend are a bit absurd. Do you honestly think that we've let noise limits dictate the weight growth of giant-scale airplanes? I was a member of IMAC's Sound Task Force and my observations are that very a significant percentage todays IMAC /TOC style airplanes care very little about sound at all. The average trend this last year was 25/50/25 cans/canister/pipes and 75/25 2-blade/3-blade. This is good because it gives us weight data points by which to test out our "3.22 is due to noise" hypotheses. I seriously doubt that the author's 40% Lanier at 37 lbs is representative of a standard 40% airplane with a super-quiet setup...I'm also certain that 24lb H9 airplane is a without cans or pipes.

Regardless I think the article is neat and it gets people thinking...I like that.

It appears that the foamies with flat or thin wings (Reynolds number independent) do follow the square-cube law pretty well from a performance standpoint but even more so from a handling qualities standpoint...this is why we think they fly so much better than the smaller airplanes of the past. The problem with many of the old scaled down balsa models is that we were afraid to change (scale-down) our building practices to get the weights right. We also were afraid to admit that ultra-thin airfoil sections work well for this situation. Actually you don't have to have a super-thin section, just a very sharp leading edge that guarantees boundary layer transition. I think over time we've intuitively learned how to more closely follow the square-cube law and we're finding that it does really work. I think you'll see now that you can build balsa models lighter than foam that has the same strength and stiffness if not more. There are obvious drawbacks when you consider ease of repair but that's another story. I think it's the repair issue that makes the foam/carbon materials the right choice. If carbon were as easy to work with as balsa then I'd probably build only carbon truss structures with super thin covering.

Great questions...thanks,
George

tmenet

George,

Hey dude... for the record I said "geeky" you must be thinking I said "kinky"! [8D] You know, I'm talking pocket protector stuff like E=mc^2, or f=ma, and P=IR and k**3, and L=W=CL*q*S=CL*rho/2*V^2*S It's how we engineers talk! Thats cool! Thats geeky!

Thanks for sharing your insight and awesome command of the subject. I learn more about aerodynamics from your forum than anywhere else. period .

I wasn't defending the authors viewpoint but rather I was trying to rationalize his direction. I really don't know what the heck he was trying to prove.

I did see where you are right that his "trend" numbers wandered into his results when he uses weight increasing by 9 times (k**3.22) instead of 8 (k**3). This resulted in the misguided conclusion that wing loading increases 2.25 times for each doubling of size instead of 2, leading him to derive that minimum airspeed must increase by 1.5 and not 1.414 as you concluded without his "trend" numbers. Why does he dodge theory and opt to modify it with such a small sample?

Anyway thanks for correcting his article and for explaining why your Ultimate and other foamies fly so well. Next I'm getting a Tensor. I'll never forget that late afternoon at the Don Lowe Masters when you flipped it over a barrier rope and kept on flying. That was awesome! Watching you guys passing the transmitter around while in a hover also blew me away!

GRH

I knew what you were talking 'bout...them's just jokes bro. LOL

One of my favorite super-geeky expressions is:

M*2.7183*r**2*(1/y)^-1

(x2)**0.5*(force/acceleration)

H*(1/a^-1)*(p^4)^(1/2) *f(x)

mu/rho 9.5x10^15 meters / c



Ya gotta luv that.



I'm not trying to bash or defend the article either...I just don't want guys to blindly follow it because it was published in MA. R/C magazine articles unfortunately don't have to go through any technical review. I kind of felt responsible because I'm the one who pointed it out to everyone so I decided to explain why the scaling factors don't coincide with the actual square-cube law. If we can get model designers to learn how to use these concepts then the airplanes will handle and perform much closer to their intended goal.

Bill Mixon

Finally got it done.
Specs. later

Bill Mixon

More..
I haven't had a chance to fly it in good weather yet, but from the flights so far I think I might have went a little too big.

GRH

WOW! Are you bringing it to SEFF?