"As the crow flies" describes the distance between two points if one could go in a straight line without needing to follow the constraints of existing roads and paths. Is there a standard phrase for the distance if one does need to stick to existing roads, that parallels "as the crow flies" and is used to contrast with it? I've only ever heard humorous "antonyms" like "It's ten miles as the crow flies, but fifteen miles as the Toyota Camry drives along Route 119."
By road would be a natural choice, as opposed to "in the air" implied by the crow.
It even has a dictionary entry and example:
In or on a road vehicle.
Lying just inside the official boundary line between the two countries, Gretna was about 350 miles by road from London.
(The distance between London and Gretna Green is around 270 miles as the crow flies)
Not an answer in the strictest sense of the question as I could not think of a common idiomatic alternative to "As the crow flies". However, a nicely balanced and easily understood alternative would be "As the road winds".
Updated to add that "As the road winds" is found commonly in text so while not strictly idiomatic it is not simply made up either.
It's five miles as the crow flies, or twelve as the road winds.
As the wolf runs maintains the same structure as the original phrase and conveys the meaning of distance on the ground. It's not a particularly commonly used phrase, but some searching did turn up some support that this is something that has been used before.
Tolkien makes use of this phrase in The Lord of the Rings.
'How far is Moria?' asked Boromir.
'There was a door south-west of Caradhras, some fifteen miles as the crow flies, and maybe twenty as the wolf runs,' answered Gandalf grimly.
The Fellowship of the Ring, Book II, chapter IV: "A Journey in the Dark" — J.R.R. Tolkien
There isn't one
There isn't one because there is no single "opposite" to "as the crow flies". The "crow" distance is the simple straight line distance and so is precisely defined but the alternatives are not interchangeable. This can be easily seen by firing up your favourite online map and asking it for the distance between two places by foot, by car, and by bike. In choosing your opposite therefore you must specify what you mean.
So "by car", "by bike", "on foot", "by rail", "by road", etc. are all valid opposites depending on what exactly you mean.
If you wish to be whimsical you can attach a suitable word to the end of these to mirror the pattern, e.g. "as the car drives", "as the bike pedals", "as the foot falls", "as the train chugs", "as the road winds", etc. None of these are widely known idioms but their intent should be easily understood.
Following roads, particularly on a grid city layout (eg NewYork), some adjective of the taxicab metric is invoked (distance, route, metric).
Would "The Scenic Route" answer the question?
"The Scenic Route" is normally used when describing a trip that does not go straight from A to B but rather takes detours during the trip to see Points C, D and E, which are placed on the route just because of the view that they give the traveller.
Hence, it's used when someone wants to take a longer route than that which is most direct.
Someone suggested "as the wolf runs", with a Tolkien reference.
A very similar phrase, that I have used more frequently is "as the fox runs". For example, this scientific paper uses it jokingly in its title Inferring the effects of potential dispersal routes on the metacommunity structure of stream insects: as the crow flies, as the fish swims or as the fox runs?
In everyday use though, I would say "driving distance" is the most common phrase, although it doesn't follow the nice structure of Dickens' "as the crow flies". However, Dickens himself didn't provide a correlate in Oliver Twist (the supposed origin of the phrase), so anything goes.
I'm not sure if this meets your criteria or not, but, I would tend to go with "circuitous route"
Circuitous having a circular or winding course - a circuitous route - a circuitous journey by snowmobile - Merriam Webster
The expression "milk run" is an common idiomatic expression with a close meaning. It has two possible components to its meaning:
- a circuitous route
- a route with a large number of stops
The first meaning is likely less often used these days, as the term is now often applied to public transit routes that make every stop in contrast to an express route that may follow the same route but make fewer stops, i.e. where the second meaning applies exclusively. However, historically I think the first meaning was more common.
In any event, it may be approximately what you are looking for. You might say, for example:
"It's 10km as the crow flies, but at least 20km by the milk-run route."
I've often seen Manhattan distance used especially in the context of programming or math. https://en.wiktionary.org/wiki/Manhattan_distance
A common British idiom for this is:
Round the houses
It's not specifically around houses, but means that a route is unnecessarily circuitous. Example:
A: How far is it to your house from town?
B: Well, it's about 5 miles as the crow flies, but there's no direct route by road. You'll have to get on the A54 to Crewe and take it from there.
A: Crikey! That takes you round the houses.
B: Yeah, but it's the only way to get over the railway lines.