How to Calculate and Solve Distance Along Great Circles | Latitude and Longitude
Last Updated on March 17, 2024
The image above represents distance along great circles. To calculate the distance along great circles, two essential parameters are needed, and these parameters are the value of R and angular difference (θ).
The formula for calculating the distance along great circles:
y = (θ / 360) x 2πR
Where;
y = Distance Along Great Circles
θ = Angular Difference
R = Radius of the Earth
Let’s solve an example;
Find the distance along great circles when the value of R is 6400, and the angular difference is 18.
This implies that;
θ = Angular Difference = 18
R = Radius of the Earth = 6400
y = (θ / 360) x 2πR
y = (18 / 360) x (2 x π x 6400)
So, y = 0.05 x 40212.38
y = 2010.6
Therefore, the distance along great circles is 2010.6 km.
Calculating the Angular Difference when the Distance Along Great Circles and the Value of R are Given
θ = y360 / 2πR
Where;
θ = Angular Difference
y = Distance Along Great Circles
R = Radius of the Earth
Let’s solve an example;
Given that the distance along great circles is 32 and the value of R is constant (6400). Find the angular difference.
This implies that;
y = Distance Along Great Circles = 32
R = Radius of the Earth = 6400
θ = y360 / 2πR
θ = (32)360 / 2π(6400)
So, θ = 11520 / 6.28(6400)
θ = 11520 / 40192
θ = 0.286
Therefore, the angular difference is 0.286°.
Read more: How to Calculate and Solve for Distance Along Small circles | Latitude and Longitude
How to Calculate Distance Along Great Circles Using Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the distance along great circles.
To get the answer and workings of the distance along great circles 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 1,500 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 Latitude and Longitude under Mathematics.
Now, Click on Distance Along Great Circles under Latitude and Longitude
The screenshot below displays the page or activity to enter your values, to get the answer for the distance along great circles according to the respective parameters which are the angular difference (θ) and value of R.
Now, enter the values appropriately and accordingly for the parameters as required by the angular difference (θ) is 18 and value of R is 6400.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the distance along great circles and presents the formula, workings and steps too.
