Mountain slope distance calculation method

Simplifying the data change at each coordinate point in the trajectory to the full trajectory data change may not be as accurate, but it can basically meet the needs. The lazy person can ignore the derivation process and look directly at the red marker formula below.

A: The derivation process and calculation formula of the slope distance for climbing

As shown in the figure, after climbing, everyone recorded trajectories can display three basic data: distance, cumulative climb and cumulative decline. Some friends would like to ask how much the actual slash distance traveled. Then let's demonstrate how to calculate the slope distance of the mountain climbing.

The cumulative climb and the uphill distance are regarded as the two right-angled sides of the right-angled triangle. The uphill slash distance is the hypotenuse. The formula for the trigonometric function is “the square of the uphill slash distance = the cumulative climb squared + the square of the uphill distance”. Out: Uphill slash distance = √ (accumulated climb squared + squared uphill distance).

Assuming cumulative climb = 1, uphill distance = 2, then the uphill slash distance = √ 5.

Assuming a cumulative decrease of 1 and a downhill distance of 3, then the downhill slope distance = √10.

The distance of the entire slash = √5+√10=5.398345638

Simplified algorithm:

In many cases, there is always a climb and a fall in the climbing process. We do not know how long the cumulative climb has taken, and how far the total distance has gone. It is difficult to distinguish between the points where the climb climbs and falls. Unless there is only climbing uphill and downhill, the ideal mountaineering route can tell how long it takes to climb and descend. So we can use the distance, cumulative climb, and cumulative drop to get the approximate full slash distance.

Slope distance = √ (square of distance + (cumulative climb + cumulative decline)) = √ (4 + 25) = √ 29 = 5.385165648

It is basically consistent with the data obtained above (the value has become smaller, reduced to less than 3/1000, 5.398345638/5.385164807=1.002448).

Mountain slope distance calculation method

If the cumulative climb is different from the cumulative decline, it is assumed that the cumulative climb = 2 and the cumulative decline = 1, the uphill distance = 2 and the downhill distance = 3.

It can be drawn that the uphill slash distance = √8. Downhill slash distance = √10.

Slope distance in the whole journey = √8+√10=5.990704785

Simplified algorithm:

The distance of full slash = √(9+25)=5.830951895

The results calculated separately from the mountain downhill are also basically consistent (the values ​​have once again become smaller, reducing to less than 3/100, 5.3990704785/5.830951895=1.027397).

Or take the one-time distance of 13 kilometers, (accumulated climbing 950 meters + cumulative decrease of 850 meters)/2 = 900 meters, and the daily climbing time of 6.5 hours as an example:

Simplified full ramp distance = √ (square of distance + (accumulated climb + cumulative decline) squared) = √ (13000 squared + (950 + 850) squared) = 13124.02377 meters. About 13.1 kilometers.

Calculate the error: 13124.02377 meters *1.027397=13483.59 meters, equal to approximately 13.5 kilometers.

The actual diagonal distance is in the range of 13.1 to 13.5 kilometers.

It can be seen that this slash distance is similar to the distance.

Finally, it is concluded that: Simplified full-length slash distance = √ (square of distance + (cumulative climb + cumulative decline) squared)