My sister is an architect and needs to use linear interpolation in the following situation:
The NCC states the maximum ramp length for a 1:14 ramp is 9 meters and a 1:20 ramp is 15 meters before you need a landing. The NCC states to calculate the maximum length of a ramp in between these gradients is to use linear interpolation.
She wants to specify a ramp of a 1:16.6 gradient and needs to calculate the maximum ramp length before needing a landing using the two values provided above. She is not confident her calculations are correct - she found the formula below but struggled to use it. So instead, she found this website - https://www.easycalculation.com/analytical/linear-interpolation.php. The solution that website provided was 11.6 meters. Can anyone confirm that this is correct and/or explain how to correctly calculate the linear interpolation for this example using the formula? Thanks in advance.
Linear interpolation = y1 + (x - x1)*(y2-y1)/(x2-x1)
Let's calculate the maximum ramp length for a 1:16.6 gradient using linear interpolation based on the two values provided: 1:14 (9 meters) and 1:20 (15 meters) before needing a landing.
First, let's assign the values:
x1 = 14 (corresponding to 1:14 gradient)
y1 = 9 meters (maximum ramp length for 1:14 gradient)
x2 = 20 (corresponding to 1:20 gradient)
y2 = 15 meters (maximum ramp length for 1:20 gradient)
x = 16.6 (corresponding to 1:16.6 gradient)
Now, we can use the linear interpolation formula:
Linear interpolation = y1 + (x - x1)*(y2-y1)/(x2-x1)
Substitute the values:
Linear interpolation = 9 + (16.6 - 14)(15-9)/(20-14)
Linear interpolation = 9 + 2.66/6
Linear interpolation = 9 + 2.6
Linear interpolation = 11.6 meters
So, according to the formula, the maximum ramp length for a 1:16.6 gradient before needing a landing is 11.6 meters. The website you mentioned provided the correct result. Linear interpolation is a useful method for estimating values between two known data points, and it's commonly used in various fields, including architecture and engineering.
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