Sometimes while navigating with map and compass, the advice is to aim off i.e. to aim either to the left or right of the intended destination, as opposed to straight for it.

Why and when would one want to do this?

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I didn't quite get your question here. I used to do a bit orienteering and one of the first things we learn is that the shortest distance between two points is a straight line but the quickest might be something else. If you're planning to reach a hut by the river, you might want to aim off towards the river so you can follow the river bed to the hut. It might be easier and safer to get to the hut. In this case is not "aiming off" it's just re routing your track – Desorder 7 hours ago
    
@Desorder imagine crossing featureless terrain to reach a non-obvioud ford in a river. When you hit the river you want to know whether the ford is to your left or right. So you pick one and aim off. The terminology is quite standard in the UK (getting off Dartmoor in fog a more realistic example) – Chris H 5 hours ago
    
Cool. Yeah. It seems we are talking about the same thing – Desorder 4 hours ago

The reason is that you could miss your destination and hit a trail and know that you are almost right, but not know which way to turn.

enter image description here

So if you were to go straight for the destination, and because of Murphy or errors or whatever and you ended up at either Point A or Point B, you wouldn't be certain of which way to turn to reach the trail intersection.

If on the other hand you had gone for Point B in the first place, you would know that when you got there, you needed to turn left. That is why one would aim off.

This works well when you are going for a single point on a well defined line like a trail or stream.

Note:

The error is exaggerated for artistic purposes, but if you were to go for the destination straight off, your margin on either side is how far you would be able to see the destination from.

On the other hand, while aiming for Point B, so long as one doesn't end up to the right of the destination, one is fine, and that is a much wider margin or error.

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In addition to the case described by Charlie (and to show that I also can make drawings in Paint), there is the case where you want a stopping line to know when you are going to far. This is mainly useful when you are aiming for the end of a feature. The drawing below is with a river bend that you try to reach, but the same principle works when aiming for the end of a trail, the end of a fence, a turn in a path etc.

Situation sketch

Obviously, the shortest way is the green line. But what happens if you deviate slightly from it to the left or the right. To the right is not an issue, but if you unknowingly deviate to the left you will end up in the situation of the red line. You should be more or less at your destination, but have no idea if you are too far or should continue a bit further. You are lost.

To avoid ending up lost, you will usually, on purpose, aim a bit to the right and follow the yellow line. It is a bit longer than the optimal green line, but you are sure that you will end up at the river. And once you hit the river you know that you should follow it a little to the left to end up at your destination. It is a bit longer than the green line, but at least you know that you will not end up in the hopeless case of the red line.

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