# How to calculate forces involved in a small fall

## Summary:

Small Scooter - How to calculate forces involved in a small fall and dimension the frame to withstand those forces.

## Main Question or Discussion Point

Hi Guys, first things first I’m Tiago
-= Introduction to my Many questions =-
I work as Inventor in several projects of small scale, doing mechanisms, 3d printing, or building them cutting, welding, using my Lathe or sending to laser cut, bending or (when lucky) sending to a local CNC, I design basic electronics and can handle electric powertrains, batteries, drivers and controllers, I handle very well Inventor or similar CAD packages.

I Have no formal training in engineering (did 2 years of Pure Math in Portugal, hated it, and a few classes on computer science in UK, still grabbing classes in EDx when I can) but got lost in the start of my career to videogame production and 3D Modelling, but gradually came back to Machines and things move and do other stuff.

I’ve been doing eyeball engineering, and that is looking to similar stuff and using the volumes and materials to achieve the same stiffness or strength, it is ok when I’m prototyping but I started to get less comfortable with this approach, and several questions have been bothering me specially because I tried to calculate them but could never validate if it was right, most people I approached, mechanics and physics professionals, where pretty evasive…

I’ve been scooped to a fun project doing electric micro vehicles, so my job initially was to prototype a scooter inside the required constrains, I’ve created two working prototypes from structure to electronics, and now I’m tasked of the third prototype that must meet strength, durability of street tests. I can do basic stress/strength analysis in software but more than that I need to know the Forces involved on those tests and after a couple of months I got courage to come here…

-= End of Small Talk =-

My scooter is a 3-wheeler with 2 in wheel Motors at the front of the scooter, it does not Tilt but has springs on each wheel.

The scooter Mass is 15 kg (it should be lower in production)

And it can support adults up to 100 Kg.

The idea is that maybe a user could just fall from a Curb to the road and this would at least keep the scooter intact, the largest curbs are around 15cm with a maximum 25cm.

So I did some research and found that I could calculate the Force of that fall using the following:

F = m.g.h

m = scoter mass + user mass = 115kg
g = 9,81m/s
h=0,25m

F = 282 Kgf

I understand that this is very simplistic and its probably the F upon reaching to the ground and nothing to do with the rest of the crash process.

My scooter has shocks and rubber to absorb 3cms (I have no idea how to dimension the strength of the shocks as as to resist the impact of r even to travel around besides the Mass divided by the 3 points of road contact.

And the person on that impact is not rigid on top of the scooter and can bend his/her Knees 15cm to absorb the shock.

And I know it can get a lot more dense, but I really don’t know what to pursuit and learn to Understand what are the maximum forced distributed to structure or even (another entirely different discipline probably.

Can you guys help me out, point me out to some learning material on this, Covid-19 has given me time to learn

Thank You,
Tiago Carita
PS - Sorry it got a bit chotic in the end has I understood the gap between what iIknow and what I need to learn...

## Answers and Replies

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berkeman
Mentor
Welcome to the PF.
Summary:: Small Scooter - How to calculate forces involved in a small fall and dimension the frame to withstand those forces.

F = m.g.h
No, PE = m * g * h is the Potential Energy that is stored in a mass held at a height h above a datum like the ground. You can use that to figure out the velocity of the object right before it hits the ground in a fall from that height, because all of that mgh PE will be converted to KE = 1/2 m * v^2.

That's a significant drop onto concrete, so it will take some pretty beefy suspension and compliant tires to survive that, especially in any repeated way. Is that really a requirement?

https://www.mountainbikesapart.com/wp-content/uploads/2014/01/mountain-bike-drop.jpg

You didn't ask, but:

One of the biggest engineering challenges in the design of a 3-wheeler is stability. The 'tip-over' axis is a line from the single wheel to the inner 'paired' wheel. The geometry is critical, and probably super-critical for a very light vehicle. Unless the curb-jump happens in a controlled way, it could be very ugly. The market for 'light' 3-wheelers in the U.S. was killed by lawsuits.

berkeman
Welcome to the PF.

No, PE = m * g * h is the Potential Energy that is stored in a mass held at a height h above a datum like the ground. You can use that to figure out the velocity of the object right before it hits the ground in a fall from that height, because all of that mgh PE will be converted to KE = 1/2 m * v^2.

That's a significant drop onto concrete, so it will take some pretty beefy suspension and compliant tires to survive that, especially in any repeated way. Is that really a requirement?

https://www.mountainbikesapart.com/wp-content/uploads/2014/01/mountain-bike-drop.jpg

View attachment 260643
It is not a requirement, it was me just trying to protect the scooter from minir acidents...

You didn't ask, but:

One of the biggest engineering challenges in the design of a 3-wheeler is stability. The 'tip-over' axis is a line from the single wheel to the inner 'paired' wheel. The geometry is critical, and probably super-critical for a very light vehicle. Unless the curb-jump happens in a controlled way, it could be very ugly. The market for 'light' 3-wheelers in the U.S. was killed by lawsuits.
That is a valueble and scary information :-/
Where could I learn more about the Geometry refered? It would be diferent if it had 4 wheels?
Its very small scooter, from the requirements, we have to use booth feets side by side and in the prototypes there are inbalances and one needs to learn not to tip the scooter, i've enven added some camber to the wheels but had no effect on the balance.

I've been talking about converting to 4 wheels but i have very strong oposition and althought i've pointed some troubles in the design i think i need to get better equiped to explain and understand the problems.

jrmichler
Mentor
now I’m tasked of the third prototype that must meet strength, durability of street tests.
It is extremely difficult to calculate the durability of a vehicle operating in the real world. There are too many variables and potential failure points. A good technique for your project is a Highly Accelerated Life Test (HALT). A HALT is just what the name implies. It subjects the object to all of the worst things that happen to it, and does so in the shortest time.

Consider what happens to a vehicle:
Hot weather (bad for batteries and motors)
Cold weather (bad for batteries and seals)
Potholes, bumps, curbs (breaks parts)
Rain
Salt (in area where it snows)
Puddles deep enough to submerge it
Long uphill on a hot day
Long downhill on a hot day
And expect that somebodies dog will pee on it

A HALT for your vehicle might involve driving over a 25 cm curb, through a puddle deep enough to submerge it, then up and over the curb again with a 100 kg person (or lighter person with a weight pack). Do this after storing at, say, 125 deg F (skip the puddle), and after storing at -40 deg (also skip the puddle). Leave it outside when it rains. If it survives 1000 curb drops, plus puddles, heat, cold, and rain, it will probably satisfy real world owners.

When running a HALT, any part that breaks must be redesigned, then the test restarted from the beginning. This can be discouraging at first, but it will result in a product that works and survives in the hands of customers.

Joe591 and berkeman
Well once again a very sound advice, one that I actually talked about with project owners, not with all this detail.
It's indeed a bit discouraging, since the requirements added to much constrains and a lot of moving parts things not easy to design specially for strength.

Thank you

berkeman
Mentor
My scooter is a 3-wheeler with 2 in wheel Motors at the front of the scooter, it does not Tilt but has springs on each wheel.
And it can support adults up to 100 Kg.

The idea is that maybe a user could just fall from a Curb to the road and this would at least keep the scooter intact, the largest curbs are around 15cm with a maximum 25cm.
Can you say why a 3-wheel design is requested? Is it just because they want it to stand up on its own? As mentioned before, the 3-wheel design is a problem to actually ride at any speed.

What kind of suspension and tires are you using so far? If you use a little bigger/softer tires, they serve as a lot of the suspension on their own. Also, the larger, softer tires handle bumps and holes and curbs a lot better than smaller, harder tires.

Can you compare and contrast your design with the more traditional electric scooter designs that are common, like the ones below? Thanks.

https://heavy.com/tech/2019/04/electric-scooter-under-500/

12 Best Electric Scooters Under \$500

Dr. Courtney
Education Advisor
Gold Member
In one dimension, impact forces are most easily estimated using the concept of stopping distance.

If the kinetic energy at impact is KE, the average force, F, over a stopping distance of d is:

F = KE/d.

Clearly, reducing the impact force usually means increasing the stopping distance. Springs or cushioned pads or inflated tires are some common approaches.

Of course, injuries and mechanical failures (stuff breaks) are more related to the peak force in the interaction rather than the average. But having studied this in many cases, it is rare for the peak force to be more than two or three times the average force when an impact brings an object to rest.

Decreasing the average stopping force by increasing the stopping distance is usually much easier than decreasing the peak to average ratio of the stopping force.

In one dimension, impact forces are most easily estimated using the concept of stopping distance.

If the kinetic energy at impact is KE, the average force, F, over a stopping distance of d is:

F = KE/d.

Clearly, reducing the impact force usually means increasing the stopping distance. Springs or cushioned pads or inflated tires are some common approaches.

Of course, injuries and mechanical failures (stuff breaks) are more related to the peak force in the interaction rather than the average. But having studied this in many cases, it is rare for the peak force to be more than two or three times the average force when an impact brings an object to rest.

Decreasing the average stopping force by increasing the stopping distance is usually much easier than decreasing the peak to average ratio of the stopping force.
So if after getting the average force*2 or *3 would be a good starting point to dimention parts before road testing?

Dr. Courtney
Education Advisor
Gold Member
So if after getting the average force*2 or *3 would be a good starting point to dimention parts before road testing?
I would suggest lab testing prototype designs before road testing. But average force *3 will be a good estimate of peak force, as long as the system does not "bottom out". Once a spring or tire or pad is fully compressed, the system has "bottomed out" and there can be a much larger spike in the peak force.

Can you say why a 3-wheel design is requested? Is it just because they want it to stand up on its own? As mentioned before, the 3-wheel design is a problem to actually ride at any speed.

What kind of suspension and tires are you using so far? If you use a little bigger/softer tires, they serve as a lot of the suspension on their own. Also, the larger, softer tires handle bumps and holes and curbs a lot better than smaller, harder tires.

Can you compare and contrast your design with the more traditional electric scooter designs that are common, like the ones below? Thanks.
Hi Bekerman.

The project is full of maniac constrains, let me give you some insights, i'm not sure what i can show...

The scooter must stand on its own because it could be remote controlled or assisted.

It should have 3 wheels because there are many people are afraid of 2 wheels (i proposed 4 then but there is a design view, you will understand later.

It must be fordable to fit another vehicle compartment that its 700mm long, 350 wide and 260/280 tall, so it’s a very short scooter as we have to slide in and out of that compartment.

That vehicle is 3-wheeler too with front traction so there is the design connection.

The tires are a bit hard as they have to motors inside them. I've used on the back a bicycle suspension oriented horizontally but for the forward wheels I’ve made several tries until I got something working and based on some military scooters I saw on the net not sure I even want to show for now :-) the major difficulty was that in the front I have traction, the axel to the direction and a huge servo to remote control, plus a system of coupling decoupling the servo.

Another constrain that impacted on the suspention is that I need a lot of internal space for batteries and all those remote control stuff and systems, i even though about using a torsion spring to the foward swing arms

I thing I should break this Post in 20 different ones just get focused opinions or to ask more cleaner answers

Back dampening was built like that.

The front is a bit more messie, I still had no money to prototype nothing from new version just digital model.

THX
Tiago

Dr. Courtney
Education Advisor
Gold Member
Hi Bekerman.

The project is full of maniac constrains, let me give you some insights, i'm not sure what i can show...

The scooter must stand on its own because it could be remote controlled or assisted.

It should have 3 wheels because there are many people are afraid of 2 wheels (i proposed 4 then but there is a design view, you will understand later.

It must be fordable to fit another vehicle compartment that its 700mm long, 350 wide and 260/280 tall, so it’s a very short scooter as we have to slide in and out of that compartment.

That vehicle is 3-wheeler too with front traction so there is the design connection.

The tires are a bit hard as they have to motors inside them. I've used on the back a bicycle suspension oriented horizontally but for the forward wheels I’ve made several tries until I got something working and based on some military scooters I saw on the net not sure I even want to show for now :-) the major difficulty was that in the front I have traction, the axel to the direction and a huge servo to remote control, plus a system of coupling decoupling the servo.

Another constrain that impacted on the suspention is that I need a lot of internal space for batteries and all those remote control stuff and systems, i even though about using a torsion spring to the foward swing arms

I thing I should break this Post in 20 different ones just get focused opinions or to ask more cleaner answers

View attachment 260765
Back dampening was built like that.

The front is a bit more messie, I still had no money to prototype nothing from new version just digital model.
View attachment 260766

THX
Tiago
It seems like the system is already strongly over constrained before considering the design needs of a key mechanical feature - resistance to anticipated mechanical loading.

Good designs start from the ground up considering and working with sound understanding of the anticipated mechanical loading. Waiting until this late in the process to understand and design for anticipated mechanical loading is a recipe for bad design.

berkeman and jrmichler
berkeman
Mentor

Back dampening was built like that.
That orientation looks incorrect to me (I could be wrong). It looks like you are wanting to use a compression spring and damper in tension mode, which I don't think will work. Shouldn't the compression spring and damper be coupled to the upper arm, with the bottom arm constrained just with a pivot?

Like typical MTB rear suspension...

https://cdn.shopify.com/s/files/1/0...oil-Cane-Creek-Coil-Close-Up.png?v=1542311444

#### Attachments

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That orientation looks incorrect to me (I could be wrong). It looks like you are wanting to use a compression spring and damper in tension mode, which I don't think will work. Shouldn't the compression spring and damper be coupled to the upper arm, with the bottom arm constrained just with a pivot?

Like typical MTB rear suspension...
Maybe the drawing is not clear ... (1) represents the axis that are fixed.
This suspention is the smalest i could find on market and work a bit diferent, not sure the name but insted of compressing you expand the connection nd the end rod compresses the spring

It seems like the system is already strongly over constrained before considering the design needs of a key mechanical feature - resistance to anticipated mechanical loading.

Good designs start from the ground up considering and working with sound understanding of the anticipated mechanical loading. Waiting until this late in the process to understand and design for anticipated mechanical loading is a recipe for bad design.
True, and i have lots of doubts in many things, someone mentioned the geometry of a three wheeled vehicle as a really complicated design, specialy if somebody decided just because...

I think the Corona gives us time to thing about it i will gather as much ammo i can to push this in the right direction.

I trully thank you all for the questions (more than any answer i could get)

TC

jrmichler
Mentor
A spring suspension system is one way to get a reasonably smooth ride and minimize impact forces.

Another way is rigidly mount the wheels on a flexible platform, similar to a skateboard with a flexible board. The flexible board could be spring steel, aluminum alloy, or fiberglass composite. All of those are available in sheets that can be sawed to size, and drilled for attachments. A composite board allows you to design for high torsional stiffness and low bending stiffness, or vice versa, if it improves your design. Another possibility is a fiber reinforced injection molded plastic board.

You would need to design the battery mounting so that board flexing would not be transmitted to the battery or its mounting.

berkeman
Mentor
insted of compressing you expand the connection nd the end rod compresses the spring
Oh, I see it now. The upward motion of the wheel pulls on the center rod (pulls on the far end of the rod), which does result in spring compression. Thanks, I've never seen that before.

Oh, I see it now. The upward motion of the wheel pulls on the center rod (pulls on the far end of the rod), which ndoes result in spring compression. Thanks, I've never seen that before.
That way i can place the shock at the bottom of the frame and get a litle bit of space on top for things...

berkeman
A spring suspension system is one way to get a reasonably smooth ride and minimize impact forces.

Another way is rigidly mount the wheels on a flexible platform, similar to a skateboard with a flexible board. The flexible board could be spring steel, aluminum alloy, or fiberglass composite. All of those are available in sheets that can be sawed to size, and drilled for attachments. A composite board allows you to design for high torsional stiffness and low bending stiffness, or vice versa, if it improves your design. Another possibility is a fiber reinforced injection molded plastic board.

You would need to design the battery mounting so that board flexing would not be transmitted to the battery or its mounting.
Unfortunatly the scooter will have an hard body shell but that idea crossed my mind i just did not heve enought knoledge to even try it, springs i think i can dimention.

I would suggest lab testing prototype designs before road testing. But average force *3 will be a good estimate of peak force, as long as the system does not "bottom out". Once a spring or tire or pad is fully compressed, the system has "bottomed out" and there can be a much larger spike in the peak force.
Gathering some of the information I reached to this average peak force if no bottoming out occurs.

I’ve assumed that the wheels rubber and springs compress 3cms and that since I have 3 contact points, I could divide the peek force by 3 and apply individually in each.

Then I will use this force to dimension the parts before any test.

But I Believe that this only applies if the Man is rigid.
Should I separate the Mans weight and lets say it will bend its knees 15cms and after calculating the average Force convert to Kgf and then calculate the scooter part using its mass plus the average force of the man?
After thinking a bit and trying out some things I got to this.

So I assumed the man would ben 15cms at the knees, and after consideration added the scooter 3cms of springs and rubber and calculated it alone

Then calculated the scooter alone and added the forces.

I really hope I ate least progressed in the right direction.

Thank you.
TC

Last edited:
Dr. Courtney
Education Advisor
Gold Member
Gathering some of the information I reached to this average peak force if no bottoming out occurs.

I’ve assumed that the wheels rubber and springs compress 3cms and that since I have 3 contact points, I could divide the peek force by 3 and apply individually in each.
Probably not a rigorous assumption, since it is equivalent to the idea that all the wheels landing at the same time (or close enough). When wheeled vehicles land after a fall, it is rare for all the wheels to land at the same time, or nearly at the same time so that the load is evenly distributed on the wheels and suspensions through the landing process.

So I assumed the man would ben 15cms at the knees, and after consideration added the scooter 3cms of springs and rubber and calculated it alone
It's not a horrible assumption to surmise that the rider bending their knees will reduce the peak loading, but without empirical data on the timing and magnitude of the biomechanical response, one risks making an overly optimistic assessment. Also consider that when estimating failure loading, you need to use a "worst case" rather than a "typical" or "average" contribution from the rider. A 15 cm knee bending is probably more optimistic than the worst case and may be more optimistic than the typical, depending on the riders.

Probably not a rigorous assumption, since it is equivalent to the idea that all the wheels landing at the same time (or close enough). When wheeled vehicles land after a fall, it is rare for all the wheels to land at the same time, or nearly at the same time so that the load is evenly distributed on the wheels and suspensions through the landing process.
True its more probable to hit with the front wheels and not at the same time. I thought dimensioning the parts would be simpler...

It's not a horrible assumption to surmise that the rider bending their knees will reduce the peak loading, but without empirical data on the timing and magnitude of the biomechanical response, one risks making an overly optimistic assessment. Also consider that when estimating failure loading, you need to use a "worst case" rather than a "typical" or "average" contribution from the rider. A 15 cm knee bending is probably more optimistic than the worst case and may be more optimistic than the typical, depending on the riders.
I have a knee injury because I’ve not bent my knees on an accident, o I should know better.

To be closer to reality I should assume then the rigidity of the rider and that we probably land on one wheel and the peek impact will be there.

That is really a huge amout of stress...

Once again thank you.
Tiago Carita

From what I’ve learn on this thread let's see if i got it.

The assumptions can be subjective and the worst case possible is total rigidity of the rider and the fall on one wheel and that the compression/dampening would be fully used on that wheel before any other wheel touches down

Total mass = 115kg
h = fall = 25cm
d = suspension compression = 3cm

PE = mph = 115*9,8*0,25=281,71J
PE= KE
Fa = KE/d = 281,75/0,03 = 9392J
Fpeek = 3*Fa = 28176J

With that number in mind I should dimension the wheel brackets to withstand a 28000 Joule impact.
And the suspention to witsand that form at maximum comprssion to avoid bottom outs.

I hope i'm on the right path.
Tiago Carita

It seems like the system is already strongly over constrained before considering the design needs of a key mechanical feature - resistance to anticipated mechanical loading.

Good designs start from the ground up considering and working with sound understanding of the anticipated mechanical loading. Waiting until this late in the process to understand and design for anticipated mechanical loading is a recipe for bad design.
Sorry to bother you Dr, Courtney, I was just wanting a help/advice on the last calculations I've made. If they are OK to the probable circumstances I’ve enunciated.

Thank you
Tiago Carita