Why Is 254 Used in the Braking Distance Formula?

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Discussion Overview

The discussion centers around the origin of the factor 254 in the braking distance formula, specifically in the context of highway safety and vehicle stopping distances. Participants explore the relationship between velocity, adherence coefficient, and the conversion of units from kilometers per hour to meters per second.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions the origin of the factor 254 in the braking distance formula.
  • Some participants suggest that 254 is a units conversion factor when velocity is measured in km/h instead of m/s.
  • Others note that the factor 254 also incorporates elements from the standard formula involving gravitational acceleration.
  • A participant expresses confusion regarding the calculations leading to the factor 254, specifically questioning the multiplication of constants.
  • Another participant clarifies that the factor 254 results from combining the gravitational constant and the conversion factor from (km/h)^2 to (m/s)^2.
  • One participant acknowledges the clarification and expresses gratitude for the explanation regarding unit conversions.
  • Another participant mentions the ease of remembering which speed conversions to apply based on the presence of the factor 254.

Areas of Agreement / Disagreement

Participants generally agree that the factor 254 involves unit conversion and gravitational considerations, but there is some confusion regarding the specific calculations and the exact nature of the factor's derivation. The discussion does not reach a consensus on the clarity of the calculations involved.

Contextual Notes

Some participants express uncertainty about the mathematical steps leading to the factor 254, indicating that further clarification may be needed regarding the conversion processes and the underlying physics.

hugo_faurand
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Hello everyone !
I'm working on my highway code and my book give me the approximate formula and the real formula of the braking distance. Here's the real formula according to the book :

$$ Bd = \frac{V^2}{254 \times f} $$

With :
V : the velocity
f : the adherence coefficient.

But I have on question. Where does this 254 come from ?

Thanks in advance.
Regards

Hugo
 
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That factor is a units conversion when V is measured in km/h instead of the usual m/s.
 
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Doc Al said:
That factor is a units conversion when V is measured in km/h instead of the usual m/s.

It's strange, usually we multiply (or divide) by 3.6 when we want to convert m/s in km/h (km/h in m/s).
 
hugo_faurand said:
It's strange, usually we multiply (or divide) by 3.6 when we want to convert m/s in km/h (km/h in m/s).
Right. That 254 is more than just a units conversion, it also contains part of the standard formula: $$\frac{V^2}{2 g \times f}$$
 
Doc Al said:
Right. That 254 is more than just a units conversion, it also contains part of the standard formula: $$\frac{V^2}{2 g \times f}$$
Sorry but I don't find the right calculus. 2*9.8 = 19.6 So I don't understand how you find this 254.
 
hugo_faurand said:
Sorry but I don't find the right calculus. 2*9.8 = 19.6 So I don't understand how you find this 254.
2*9.8 takes care of the 2g factor. Now include the conversion from (km/h)^2 to (m/s)^2. That requires multiplying by (1/3.6)^2, which gives you a constant of 2*9.8*3.6^2 = 254 in the denominator.
 
Doc Al said:
2*9.8 takes care of the 2g factor. Now include the conversion from (km/h)^2 to (m/s)^2. That requires multiplying by (1/3.6)^2, which gives you a constant of 2*9.8*3.6^2 = 254 in the denominator.

AH I see. Highway code should tells us the unit of V. Thank you ! :)
 
Great answer. I have also been wondering where the 254 comes from. Now its easier to remember which speed to convert with 3.6 or 0.27778 and which speed does not require conversion because the factor is alredy included in either 254 or 3.6 or 0.694 (TeV). Thank you.
 

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