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Converting a RC cars specs to a 1:1 car?

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Just for fun I was thinking the other day what kind of performance a real car would have if one would convert the specs from a RC car?

I was never good at math but I guess it would be possible to calculate since we know the weight contra the specs fof the motor.

As an example I put my Blitzer Beetle on a weight today (all radio grear and battery included) and it came to 1.830 kg

Im currently running a standard 540 silver can that IIRC has 0.025 Nm running on 7.2 Nimhs.

Could be interesting what kind of horsepower that would be on a real car:)

 

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Most kits are in 1/10th scale.  

0.025Nm is 0.25 kg/cm torque.  Times 10 = only 2.5kg/cm torque. But it's only weighs 1.8kg. 10 times that is only 18kg.  A yellow labrador would weigh twice that, lol... 

I have a feeling that converting speed might be better?  If it runs 18km/h, in real life, it would be 180km/h. (110mph)

As some members had done, if you can make it go 100km/h, in real life that's 1000km/h or about Mach 0.8!  That's cruising speed of a jetliner.  

 

 

 

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I was was watching a video on the tube and a gentleman with permission from Tyrel built a new 6 wheel F1 Tyrel. He used the Tamiya 1/12 Tamiya instructions to fill in the blanks where he didn’t have the drawings!

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18 hours ago, Juggular said:

Most kits are in 1/10th scale.  

0.025Nm is 0.25 kg/cm torque.  Times 10 = only 2.5kg/cm torque. But it's only weighs 1.8kg. 10 times that is only 18kg.  A yellow labrador would weigh twice that, lol... 

I have a feeling that converting speed might be better?  If it runs 18km/h, in real life, it would be 180km/h. (110mph)

As some members had done, if you can make it go 100km/h, in real life that's 1000km/h or about Mach 0.8!  That's cruising speed of a jetliner.  

 

 

 

Whilst good for marketing, scale as it relates to speed has never been an accurate statistic,  because amongst other things it ignores that aerodynamic drag and mass do not increase in a linear fashion.

To get a better idea of what a 1/1 version of an RC car would be, let’s first understand some basic maths and use the example of a snooker table’s surface area (2 axes) at three common sizes:

- A full size snooker table is 12ft x 6ft, and has a surface area of 72sqft.

- A 3/4 size snooker table is 9ft x 4.5ft and has a surface area of 41.5sqft or ~57.6% that of a full size table.

- A 1/2 size snooker table is 6ft x 3 ft and has a surface area of 18sqft or ~25% that of a full size table.

With the above in mind, let’s give an rc car some values that we can appropriately scale:

- A typical TT-02 club racer has a mass of 1.35kgs.

- Let’s make the TT-02 a cube for ease and give it an assumed volume of 1 (1w x 1h x 1d).

To calculate density we rearrange the formula mass = density x volume as density = mass / volume so density = 1.35 / 1 meaning density is 1.35.

To the 1/1 scale vehicle then, we have to multiply the volume by a factor of 10 in each axis so 10w x 10h x 10d gives us a volume of 1000. Which allows us to calculate mass as being 1350kg (1.35 x 1000).

To work out the top speed of a 1/1 version then, we’d need to understand how each other factor of the car changes with scale but it wouldn’t simply be 1/10 speed multiplied by 10.

If you wanted to calculate the mass of any RC car at 1/1 scale, and simplifying the above to do so, put your car on a scale and weigh it then follow the formula below relative to whatever size your RC car is:

1/12 scale mass x 1728

1/10 scale mass x 1000

1/8 scale mass x 512

1/5 scale mass x 125

If you’ve a vehicle at any other scale and want to calculate its mass at 1/1, cube the value on the right side of the scale and you’ll get your multiplier.

Anyway, that was very long winded, resolves nothing and took me an age to type.

Thank you for coming to my TED Talk!

Luke

Edited by lukej
I made a maths error!
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Somewhat on topic-ish, sort of hah..   I remember on one of James May's toy shows, he made a 1:1 Airfix kit of a Spitfire by scaling up the original kit. 

So a 1:1 polycarbonate bodyshell would be fun to see 🤔 

 

... anyway, back to the maths!

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Remember the 10th scale to full size is increased in all three dimensions, length, width and height so 10^3 = 1000. 

Your 1.8kg model at full scale would be 1,800kg.

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Strength on parts like suspension arms are closely correlated to cross sectional area. As you go from 1:10 to 1:1 the cross sectional increases x 100 whilst the mass they have to support is increased 1000 time so everything needs to be much thicker or made of better materials. 

However we do have cars like the Tesla to compare. I wonder what power they put out? Interestingly they are around 1800 kg so around 1000 times heavier than an 1:10 rc car so if they could produce 1000 x the power you could imagine having similar acceleration at least.

I'm not sure how scaling up a 540 motor from 1:10 to 1:1 would work. It would weigh 1000 times more but could it produce 1000 times the power?

 

 

 

 

 

 

 

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While mess/volume/weight is to the power of 3 (3 dimensions), speed is still x 10 isn't it? As it is still in one dimension. So a 40mph RC car is 400mph in 1:1?

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1 hour ago, Nikko85 said:

Strength on parts like suspension arms are closely correlated to cross sectional area. As you go from 1:10 to 1:1 the cross sectional increases x 100 whilst the mass they have to support is increased 1000 time so everything needs to be much thicker or made of better materials. 

However we do have cars like the Tesla to compare. I wonder what power they put out? Interestingly they are around 1800 kg so around 1000 times heavier than an 1:10 rc car so if they could produce 1000 x the power you could imagine having similar acceleration at least.

I'm not sure how scaling up a 540 motor from 1:10 to 1:1 would work. It would weigh 1000 times more but could it produce 1000 times the power?

 

A top end Tesla can put out maybe 1000bhp, lets say 750kW. A 540 can maybe do 0.2kW, so the tesla can output ~ 3,750 time the power. 

However just the kinetic energy to get a speed is 1/2mV^2 (a squared on velocity). So accelerating 100mph vs 10mph you need 100 times the energy input.

So when in a 1:1 car you've got 1000 times the mass and need 100 times the energy (10mph vs 100mph) you can see why 1/10 cars have a massive advantage. 

Example;

A 2kg 1/10 doing to 10mph needs about 20 Joules of energy.

A 2000kg Tesla to 100mph need 2.000,000 Joules of energy. (100,000 times the energy)

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51 minutes ago, Xeostar said:

A top end Tesla can put out maybe 1000bhp, lets say 750kW. A 540 can maybe do 0.2kW, so the tesla can output ~ 3,750 time the power. 

However just the kinetic energy to get a speed is 1/2mV^2 (a squared on velocity). So accelerating 100mph vs 10mph you need 100 times the energy input.

So when in a 1:1 car you've got 1000 times the mass and need 100 times the energy (10mph vs 100mph) you can see why 1/10 cars have a massive advantage. 

Example;

A 2kg 1/10 doing to 10mph needs about 20 Joules of energy.

A 2000kg Tesla to 100mph need 2.000,000 Joules of energy. (100,000 times the energy)

A Tesla does come with bearings as standard though 😉

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1 hour ago, alvinlwh said:

While mess/volume/weight is to the power of 3 (3 dimensions), speed is still x 10 isn't it? As it is still in one dimension. So a 40mph RC car is 400mph in 1:1?

Nope, aerodynamic drag doesn’t rise in a linear fashion, friction losses grow as does inertia. Oh, and traction (assuming tyres were equal) would stay the same.

Luke

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9 hours ago, lukej said:

A full size snooker table is 12ft x 6ft, a

 

9 hours ago, lukej said:

A 1/2 size snooker table is 4.5ft x 3 ft

Shouldn't a 1/2 size snooker table be 6ft x 3ft?

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1 minute ago, Tamiyastef said:

 

Shouldn't a 1/2 size snooker table be 6ft x 3ft?

Yes 😂

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Just now, lukej said:

Yes 😂

Thanks, I thought I was lost 😁

Rest of the math though is above my abilities 🤪

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40 minutes ago, Tamiyastef said:

Thanks, I thought I was lost 😁

Rest of the math though is above my abilities 🤪

Yeah I just halved the number above not the full size! That’ll teach me not to check my working out!

Luke

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Aha!  That's good.  As far as the mass is concerned, it makes good sense. 

(As a side note, I've noticed that when picture files go down 50%, they mean 50% of the height and 50% of width. Not 50% of the area. The resulting memory size --which would be equivalent to area-- goes down to 25%. Just like the pool table analogy. )  That explains why RC cars don't fly off to the Moon. The mass is actually scale! 

But as @alvinlwh raised, while mass grows in 3 dimension, the speed wouldn't be 3 dimensional. The car does not grow tall or fat as it runs.  It just shoots forward.  So I would assume 18km/h would translate to 180km/h (if the Beetle's chassis length is exactly 1/10th). 

If a 1 meter RC chassis (most are only 30-40cm, but let's call it 1m for the ease of calculation) covers 100times its own length in 1 minute, that's 0.1km in 1 minute. After 60 minutes, 6km/h.  Blow it up to the real 1:1 size, the chassis would be 10m long.  If it covers 100 times its own length, that's 1km.  Doing it in 1 minute means 60km/h.  It wouldn't be 6000 km/h.  If time is the same, the scale speed would be a simple multiplication.  

ooh, unless time changes or the metric changes... that would be a wonky calculation.    

Anybody remember these shrinking movies?  Since I was thinking about re-sizing, they came to me.  I can't believe I'm so old, movies I enjoyed watching were made 37 years ago.  "Inner Space" was a remake of even older movie, Fantastic Voyage (1966). 

pFVZJP4.jpg

12GwOjy.jpg

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2 hours ago, Juggular said:

But as @alvinlwh raised, while mass grows in 3 dimension, the speed wouldn't be 3 dimensional. The car does not grow tall or fat as it runs.  It just shoots forward.  So I would assume 18km/h would translate to 180km/h (if the Beetle's chassis length is exactly 1/10th).

It doesn’t scale, because drag losses square with speed and as such grow rapidly with both speed and area.

To be honest, this is where the algebra goes from high-school to university levels and if we were to calculate drag as it relates to all aspects of a car we end up down a rabbit hole looking at friction losses across drivetrains etc., anyway.

To calculate the aerodynamic drag acting on the car, we use the equation:

Fd = 0.5 x p x u^2 x A x Cd

for reference:

Fd = drag force (N)

p = liquid density (kg/m^3)

u = relative velocity (m/s)

A = reference area (cm^2)

Cd = drag coefficient 

To make things simple, we can plug in the numbers based on the previously referenced TT-02 club racer, as ever this will combine some true values with some assumed ones, as below:

p = 1.204 (approximately the density of air)

u = 27.778 (100kph in m/s)

A = 199.5*

Cd = 1.05 (the drag coefficient of a cube/cuboid)

*To approximate area I measured a standard Tamiya 1:10 Touring body (Subaru BRZ R&D Sport #59607), but made it a cube to ease the calculation for both area (A) and coefficient of drag (Cd).

So for a 1/10 cube of a Subaru BRZ RC car, the aerodynamic drag at 100kph is calculated as:

0.5 x 1.204 x 27.778^2 x 199.5 x 1.05, giving us an Fd of 9.73N

To show the relationship with speed, if we halve the velocity to 13.889m/s, we get a value of 2.4326N. Equally, if we increase the speed to 55.556m/s, we get a value of 38.92N.

Now, if we scale the car up to 1/1, multiply the frontal area by 100, so 199.5 becomes 19,950 and so the equation is:

0.5 x 1.204 x 27.778^2 x 19,950 x 1.05, giving us an Fd of 973N.

As I said at the top of the comment, drag squares with speed, so at 13.889m/s, we get a value of 243.26N and at 55.556m/s, we get a value of 3892N.

This also touches on what @Nikko85 said about cross sectional area, so when we take a 1/10 car and scale it to 1/1 we now have to deal with a car 1000 times the weight, with components that have 100 times the cross sectional area, and an aerodynamic drag penalty that’s also 100 times as much. With all this to overcome, you can quickly see how speed can be lost.

There ends my second TED Talk 😂

Luke

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Hi,

The area in your calcs only needs the frontal plan area not the surface area of the whole cube. The sides, top, bottom and back have drag but it's much lower.

 

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1 hour ago, Xeostar said:

Hi,

The area in your calcs only needs the frontal plan area not the surface area of the whole cube. The sides, top, bottom and back have drag but it's much lower.

 

Hi,

Thats exactly as they’re set up.

Luke

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10 hours ago, lukej said:

Hi,

Thats exactly as they’re set up.

Luke

It's your area units, in your equation as stated area needs to be in m2 , but you do note cm2 but then omit the /10,000 in the equation to compensate for the area units. 

199.5 seemed a big number for a rc car in m2

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On 2/26/2023 at 4:25 PM, Xeostar said:

A top end Tesla can put out maybe 1000bhp, lets say 750kW. A 540 can maybe do 0.2kW, so the tesla can output ~ 3,750 time the power. 

What's interesting is that this means a 250 bhp car has then roughly both 1000 x the mass and power of an RC car.

The question for me is if you scaled up a 540 motor to 1:1 how powerful would it be? If it is 1000 then you have your answer;  a 1:1 rc car would be roughly the same size and weight as a 1:1 car with a 250 bhp engine, and so instead of just scaling everything up from 1:10 you can take it from there.

You have all the data on a 1:1 car, so it makes the maths somewhat easier.

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@lukej brought up another interesting point!  

The air molecules don't shrink!  (I'm reminded of old movies of naval warfare where water splashes are huge because they filmed scale models.)  Small RC cars will face a lot less air resistance.  I once tried to figure out the air resistance of 6mm vs 8mm BBs.  3.14x3x3 = 28   3.14x4x4= 50.  Mere 2mm difference made the area twice as large.  For a tiny 2.5g projectiles, that makes a whole lot of difference.  

So yeah, the air resistance would be huge. (Bicycles speed up twice if there is a wind blocking vehicle in front)

 

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12 hours ago, Xeostar said:

It's your area units, in your equation as stated area needs to be in m2 , but you do note cm2 but then omit the /10,000 in the equation to compensate for the area units. 

199.5 seemed a big number for a rc car in m2

I see what you’re saying, thank you. Turns out the force outcomes were correct, but the area in the equation wrong - frontal area was 199.5cm^2, so yes it needs that adjustment.

To be honest, I was relying on tired 4am brain and Engineers Toolbox to do the maths I wasn’t quite awake enough for. One day I’ll learn!

On a separate point, the cube was used for consistency with previous equations, so yes, we could have just used the frontal area but a vertical plane has a worse coefficient (1.17).

With that said, it’s an irrelevance because and car would have a much better profile than a cube anyhow (a road going BRZ has a Cd of 0.27).

Luke

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'Scale speed' means a tenth scale model will only travel 1/10th as fast as the full size car.    I used the formulas shown by Lukej and applied the scale speed for a 10th scale model to produce the table below.   I made an assumption the model will have worse performance than a full size car in aspects such as Cd (drag co-efficient) and drive train losses.    However the full size car has an enormously worse aerodynamic drag.  The hypothetical full size car requires 260kW engine power to travel at 300km/h.   The model only requires 4.7W to travel at scale speed of 30km/h, which seems feasible considering a 540 motor will be lightly loaded at maximum RPM.   The electric power consumption will be higher than this figure due to the inefficiency of the electric motor.   Please let me know if you can offer any correction of comments.

 

 

 

Power requirement2.jpg

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