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Blondel's Law
Description 
In the 17th century, the architect François Blondel [1] studied the relationship between the the riser ($h$) and the the tread ($d$) of a staircase to ensure it was comfortable for the user.
He discovered that the relationship had to meet the following equation:
| $2 h + d = c_2 $ |
where the blondel constant (2) ($c_2$) must be between 63 and 65 cm.
To achieve greater comfort, it was also necessary to meet the blondel constant (1) ($c_1$), which should be around 46 cm, establishing that the relationship was:
| $h + d = c_1 $ |
[1] Cours dArchitecture, François Blondel, L'Académie Royale de Arquitecure, 1675
ID:(957, 0)
Number of steps and length of the ladder
Description
The number of steps ($n$) depends on the stair height ($H$) and the riser ($h$) as it represents the number of times the latter fits into the total height:
| $n = \displaystyle\frac{ H }{ h }$ |
Given the tread ($d$), the staircase length ($L$) can be calculated using the following formula:
| $ L = n d $ |
ID:(958, 0)
The spiral staircase
Description
In a spiral staircase with a diameter of the staircase radius ($R$), people walk along a radius equal to the walking radius ($r$):
This radius is calculated as follows:
| $r = \displaystyle\frac{2 R }{3}$ |
If the step is described as an element of the circle:
we find that the step angle ($\theta$) together with the tread ($d$) is equal to:
| $ \theta = \displaystyle\frac{ d }{ r } $ |
This, in turn, defines the full turn ($\Omega$) through:
| $ \Omega = n \theta $ |
ID:(959, 0)
Model
Description
Parameters
Variables
Calculations
to 
, then, select the variable: 
to 
Calculations
Calculations
Variable 
Given Calculate 
Target : Equation To be used 
Equations
$ L = n d $
L = n * d
$n = \displaystyle\frac{ H }{ h }$
n = H / h
$ \Omega = n \theta $
Omega = n * theta
$r = \displaystyle\frac{2 R }{3}$
r = 2* R /3
$ \theta = \displaystyle\frac{ d }{ r } $
theta = d / r
$2 h + d = c_2 $
2* h + d = c_2
$h + d = c_1 $
h + d = c_1
ID:(956, 0)
Blondel's Law
Equation
In the 17th century, architect François Blondel formulated the relationship between the the riser ($h$) and the tread ($d$) of a staircase to ensure its comfort:
| $2 h + d = c_2 $ |
where the blondel constant (2) ($c_2$) is approximately 63 cm.
ID:(949, 0)
Blondel's second law
Equation
There is a second law by architect François Blondel that, to achieve greater comfort, states that the relationship between the riser ($h$) and the tread ($d$) should be:
| $h + d = c_1 $ |
where the blondel constant (1) ($c_1$) is approximately 46 cm.
ID:(950, 0)
Number of steps
Equation
If the stair height ($H$) and the riser ($h$) are known, the number of steps ($n$) can be calculated using the following formula:
| $n = \displaystyle\frac{ H }{ h }$ |
ID:(951, 0)
Walking radius
Equation
If the staircase radius ($R$) is known, the walking radius ($r$) can be calculated using the following formula:
| $r = \displaystyle\frac{2 R }{3}$ |
ID:(952, 0)
Staircase length
Equation
The staircase length ($L$) can be calculated from the number of steps ($n$) and the tread ($d$) using the following formula:
| $ L = n d $ |
ID:(953, 0)
Angle per step
Equation
The step angle ($\theta$) can be calculated from the tread ($d$), which corresponds to the arc, and the walking radius ($r$) using the following formula:
| $ \theta = \displaystyle\frac{ d }{ r } $ |
ID:(954, 0)
Full turn
Equation
The full turn ($\Omega$) is obtained from the number of steps ($n$) and the step angle ($\theta$) using the following formula:
| $ \Omega = n \theta $ |
ID:(955, 0)