# Wheel spin up force calculation

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#### Arbalete

##### New Member
Hi everyone

I need to calculate the drag force on a nose wheel strut caused by wheel spin up at touch down. Any hints where I should look for an explanation?

Stefan

#### Dana

##### Super Moderator
Staff member
I'd start with the weight on the nosewheel times the coefficient of friction of a tire on concrete as a conservative estimate.

#### ragflyer

##### Well-Known Member
I generally use Hiscocks (Design of light aircraft) for all things loads. I would recommend this book highly if you do not have it. He gives the drag force as 0.8* vertical load. I think it is based on VLA standard though not 100% sure.

#### ragflyer

##### Well-Known Member
I just confirmed the above formula (post #3) is indeed taken by Hiscocks from the VLA standard (page 60).

#### Arbalete

##### New Member
That dead simple? But it seems right. I must have been looking way too far.
I am getting rather moderate values which I can handle easily in my construction.

Thanks a lot

#### Hot Wings

##### Grumpy Cynic
HBA Supporter
Log Member
For force during spin-up you will need both the friction coefficient and the rotational inertia of the tire/wheel assembly..................maybe even the spring rate to make a formula for the friction during transition. sounds like a lot of work.

But as Dana noted the friction coefficient may be the limiting factor. Here is what ASTM has to say about the nose wheel for LSAs:

#### ragflyer

##### Well-Known Member
btw very interesting and dare I say audacious project, Stefan. It is amazing the progress you have made almost single handedly. Big fan of wooden airplanes and will be closely following your build.

#### ragflyer

##### Well-Known Member
Was a little concerned as the VLA and LSA standard is for small airplanes and your project is much larger. However even the Part 23 standard gives the same formula, so I guess it is well established across various categories.

#### ragflyer

##### Well-Known Member
For force during spin-up you will need both the friction coefficient and the rotational inertia of the tire/wheel assembly..................maybe even the spring rate to make a formula for the friction during transition. sounds like a lot of work.

But as Dana noted the friction coefficient may be the limiting factor. Here is what ASTM has to say about the nose wheel for LSAs:
View attachment 118861
yes that is identical to the VLA formula. The vertical load is 2.25 times the static load and 0.8*2.25 = 1.8.

#### Arbalete

##### New Member
Thanks Ragflyer. The project is rather ambitious but it's absolutely exciting working with capabilites like all you guys here.
Hot Wings. Thanks for the sketch. I will put that into my statement for the nose gear (re)construction.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
FAR Part 23 had a method for calculating spin up reactions. 23.479 cited methods detailed in Appendix C and Appendix D. Appendix C implies aft reaction at 1/4 of the vertical load on each wheel. Appendix D uses a formula. Pazmany's Landing Gear for Light Aircraft summarizes all of this nicely. Appendix D states that spin up loads need not exceed 0.8 time vertical loads, while Appendix C seems to imply a minimum of 0.25 times vertical load.

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#### Highplains

##### Well-Known Member
So close to the treadmill thought problem.

##### Well-Known Member
I'd start with the weight on the nosewheel times the coefficient of friction of a tire on concrete as a conservative estimate.
You took the words right out of my mouth!

#### Tiger Tim

##### Well-Known Member
I'd start with the weight on the nosewheel times the coefficient of friction of a tire on concrete as a conservative estimate.
He gives the drag force as 0.8* vertical load.
Appendix D states that spin up loads need not exceed 0.8 time vertical loads,
Seems to all line up pretty well, isn’t the coefficient of friction for rubber on dry concrete about 0.8?

#### Arbalete

##### New Member
Here's the outcome. If all the calculations were that simple!

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#### wsimpso1

##### Super Moderator
Staff member
Log Member
Seems to all line up pretty well, isn’t the coefficient of friction for rubber on dry concrete about 0.8?
It can be much higher. Many production cars an motorcycles have achieved decels greater than 1 g for decades, which means COF substantially greater than unity.

Airplane tires have high unit loading on the tread patch, and won't get as high. I would view 0.8 as an upper bound.