How to Calculate and Solve for Elevation of a Point | Land Development
Last Updated on April 18, 2024
The image above represents elevation of a point. To calculate elevation of a point, five essential parameters are needed and these parameters are Elevation at the Origin (a), Slope in x direction (Sx), Slope in y direction (Sy), Distance from origin (X) and Distance from origin (Y).
The formula for calculating elevation of a point:
E = a + SxX + SyY
Where:
E = Elevation of a Point
a = Elevation at the Origin
Sx = Slope in x direction
Sy = Slope in y direction
X = Distance from Origin
Y = Distance from Origin
Let’s solve an example;
Find the elevation of a point when the elevation at the origin is 2, the slope in x diection is 5, the slope in y direction is 9, the distance from origin is 7 and the distance from origin is 3.
This implies that;
a = Elevation at the Origin = 2
Sx = Slope in x direction = 5
Sy = Slope in y direction = 9
X = Distance from Origin = 7
Y = Distance from Origin = 3
E = a + SxX + SyY
That is, E = 2 + (5)7 + (9)3
E = 2 + 35 + 27
E = 64
Therefore, the elevation of a point is 64.
Calculating for the Elevation at the Origin when the Elevation of a Point, the Slope in x Direction, the Slope in y Direction, the Distance from Origin and the Distance from Origin are Given
a = E – SxX – SyY
Where;
a = Elevation at the Origin
E = Elevation of a Point
Sx = Slope in x direction
Sy = Slope in y direction
X = Distance from Origin
Y = Distance from Origin
Let’s solve an example;
Find the elevation at the origin when the elevation of a point is 40, the slope in x direction is 2, the slope in y direction is 4, distance from origin is 10 and the distance from origin is 3.
This implies that;
E = Elevation of a Point = 40
Sx = Slope in x direction = 2
Sy = Slope in y direction = 4
X = Distance from Origin = 10
Y = Distance from Origin = 3
a = E – SxX – SyY
Then, a = 40 – (2)(10) – (4)(3)
a = 40 – 20 – 12
a = 8
Therefore, the elevation at the origin is 8.
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Calculating for the Slope in x Direction when the Elevation of a Point, Elevation at the Origin, the Slope in y Direction, the Distance from Origin and the Distance from Origin are Given
Sx = E – a – SyY / X
Where;
Sx = Slope in x direction
E = Elevation of a Point
a = Elevation at the Origin
Sy = Slope in y direction
X = Distance from Origin
Y = Distance from Origin
Let’s solve an example;
Find the slope in x direction when the elevation of a point is 62, the elevation at the origin is 14, the slope in y direction is 3, the distance from origin is 12 and the distance from origin is 2.
This implies that;
E = Elevation of a Point = 62
a = Elevation at the Origin = 14
Sy = Slope in y direction = 3
X = Distance from Origin = 12
Y = Distance from Origin = 2
Sx = E – a – SyY / X
Sx = 62 – 14 – (3)(2) / 12
That is, Sx = 62 – 14 – 6 / 12
Sx = 42 / 12
Sx = 3.5
Therefore, the slope in x direction is 3.5.
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Calculating for the Slope in y Direction when the Elevation of a Point, the Slope in x Direction, the Elevation at the Origin, the Distance from Origin and the Distance from Origin are Given
Sy = E – a – SxX / Y
Where;
Sy = Slope in y direction
E = Elevation of a Point
a = Elevation at the Origin
Sx = Slope in x direction
X = Distance from Origin
Y = Distance from Origin
Let’s solve an example;
Find the slope in y direction when the elevation of a point is 58, the elevation at the origin is 15, slope in x direction is 5, distance from origin is 3 and the distance from origin is 20.
This implies that;
E = Elevation of a Point = 58
a = Elevation at the Origin = 15
Sx = Slope in x direction = 5
X = Distance from Origin = 3
Y = Distance from Origin = 20
Sy = E – a – SxX / Y
Sy = 58 – 15 – (5)(3) / 20
This means Sy = 58 – 15 – 15 / 20
Sy = 28 / 20
Sy = 1.4
Therefore, the slope in y direction is 1.4.
Calculating for the Distance from Origin when the Elevation of a Point, the Slope in x Direction, the Slope in y Direction, the Elevation at the Origin and the Distance from Origin are Given
X = E – a – SyY / Sx
Where;
X = Distance from Origin
E = Elevation of a Point
a = Elevation at the Origin
Sx = Slope in x direction
Sy = Slope in y direction
Y = Distance from Origin
Let’s solve an example;
Find the distance from origin when the elevation of a point is 66, the elevation at the origin is 8, the slope in x direction is 2, the slope in y direction is 7 and distance from origin is 3.
This implies that;
E = Elevation of a Point = 66
a = Elevation at the Origin = 8
Sx = Slope in x direction = 12
Sy = Slope in y direction = 7
Y = Distance from Origin = 3
X = E – a – SyY / Sx
X = 66 – 8 – (7)(3) / 12
Then, X = 66 – 8 – 21 / 12
X = 37 / 12
X = 3.08
Therefore, the distance from origin is 3.08.
Calculating for the Distance from Origin when the Elevation of a Point, the Slope in x Direction, the Slope in y Direction, the Elevation at the Origin and the Distance from Origin are Given
Y = E – a – SxX / Sy
Where;
Y = Distance from Origin
E = Elevation of a Point
a = Elevation at the Origin
Sx = Slope in x direction
Sy = Slope in y direction
X = Distance from Origin
Let’s solve an example;
Find the distance from origin when the elevation of a point is 72, the elevation at the origin is 13, the slope in x direction is 9, the slope in y direction is 16 and the distance from origin is 2.
This implies that;
E = Elevation of a Point = 72
a = Elevation at the Origin = 13
Sx = Slope in x direction = 9
Sy = Slope in y direction = 16
X = Distance from Origin = 2
Y = E – a – SxX / Sy
Y = 72 – 13 – (9)(2) / 16
That is, Y = 72 – 13 – 18 / 16
Y = 41 / 16
Y = 2.56
Therefore, the distance from origin is 2.56.
How to Calculate Elevation of a Point in Land Development Using Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the elevation of a point.
To get the answer and workings of the elevation of a point using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.
You can get this app via any of these means:
Web – https://www.nickzom.org/calculator-plus
To get access to the professional version via web, you need to register and subscribe for NGN 2,000 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator
Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Agricultural under Engineering.
Now, Click on Land Development under Agricultural
Now, Click on Elevation of a Point under Land Development
The screenshot below displays the page or activity to enter your values, to get the answer for the elevation of a point according to the respective parameters which is the Elevation at the Origin (a), Slope in x direction (Sx), Slope in y direction (Sy), Distance from origin (X) and Distance from origin (Y).
Now, enter the values appropriately and accordingly for the parameters as required by the Elevation at the Origin (a) is 2, Slope in x direction (Sx) is 5, Slope in y direction (Sy) is 9, Distance from origin (X) is 7 and Distance from origin (Y) is 3.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the elevation of a point and presents the formula, workings and steps too.
