I'm trying to calculate the distance between the WGS84 meridian at 51°28′40.1″N 0°0′5.3″W and the actual prime meridian at 51°28′40.1″N 0°0′0″W in feet. Wiki claims the two points are 5.3'' from each other. My calculation below results in 334 feet and this differs from Wiki's answer of 336.21 feet. I looked at Google maps and used the measure feature, after which I measured 190 feet between both coordinates and this is pictured.
Does anyone know how to correctly calculate this and why the differences between Google, Wiki and my calculation?
$1^\circ = 60′ = 60\,\text{nm} = 69\,\text{mi}$
$1′ = 60″ = 1\,\text{nm} = 1.15\,\text{mi}$
$1″ = 60″′ = 1/60\,\text{nm} = 101.2\,\text{feet}$
$5.3'' \cdot 101.2\,\text{feet} * cos(51.47°) = 334\,\text{feet}$
Best Answer
You have used the simple rule $$1' = 1\ \text{nm}.$$ This rule is correct for distances in north-south direction. But for distances in west-east direction it is not so simple.
You need to consider the fact that neighboring meridians don't have a constant distance. (Just look at a globe to understand this.) Instead, the meridians get closer and closer to each other, when walking away from the equator towards the north or south pole. At the equator you have $$1' = 1\ \text{nm}.$$ But going away from the equator the correct rule for west-east distances becomes $$1' = \cos(\phi)\cdot 1\ \text{nm}$$ where $\phi$ is the geographical latitude. In your case you have $\phi=51.47°$, and hence $\cos(\phi)=0.6228$.