Why would some bikes come equipped with a smaller front wheel?
I saw a Miyata 615 touring bike with 700c rear wheel and 24" front wheel.
I wonder what is the reason for this size for the front wheel. For touring it is ideally unsuitable as the rider needs to carry 2 sizes of spare tubes and possibly tires.

ak08820, Smaller front wheels have been used on some very small frames and on some time trial/tri bikes. I don't think it would be a major item to account for.

Brad

When Bill Boston began building bikes bikes for short statured riders back in the 1970s, he developed the small front wheel (to size the bike to the rider without unusual, strange handling geometry) and standard size rear wheel (because he was working with five speed freewheels with 14T small cogs) design.

With the availability of hybrid hubs and cogs as small as 9T, it's no longer necessary to use a standard size (27" or 700C) rear wheel to get acceptable high gear ratios, and good handling bikes without toe overlap can be built for short statured riders with two equal sized, smaller diameter wheels. In fact, the 'small front wheel, large rear wheel' has been an anachronistic design since the early 1980s. Some manufactures continued to build bikes this way for decades, though, as sort of a 'marketing signature'.

it is for geometry, so that one doesnt have toe overlap with the front wheel on a small frame, and to keep the seat post frame angle at not too much of a steep angle, also so the headtube area of the frame isnt too squarshed.

take a look at the Terry website (bikes for women) as there used to be videos made by the founder, one of which explains in simple terms with her making rudimentary drawings, to explain the reason why small frames work well with smaller front wheels.
My wifes XS frame she just got does have toe overlap, but I figure it depends on the rider on how they adapt to this and learn not to have their foot forward at a snails pace when the wheel will actually get turned a lot to either side.

I seriously thought about a Terry bike for my wife, but in the end we didnt go that route, partly because they are not in stores here, so no way to actually see and try one (and to be honest, was a bit offput by having yet another set of tires and tubes in the house, we already have 24 inchers, 26ers, 700x25, 28, 32s, even borrowed a 650 bike for a while.....so its already easy enough to make a mistake in grabbing spare tubes etc.

I had a Lotus Elite 600 that had a 700c rear and a 24" front to prevent toe overlap and allow the TT to have the traditional flat angle(or lack thereof) of a road bike. I am short and the bike was a 44cm. The smaller front wheel made it sortof squirrely though and yes, you needed to carry 2 tubes instead of 1. I liked the funky clown look of it though and sometimes when I rub my toes on a turning front 700c wheel of my replacement Casseroll, I miss the 24" front. But I never feel out of control at high speeds on the Cass like I did on the Lotus.

My wife has a Miyata 512 with a 24" front wheel. By using a smaller wheel, the frame can be proportioned coreectly for a shorter rider. I see similar bikes come up on the local Craigslist from time to time.