Wood-stove advocates like them because you dont have to carry fuel, and fuel is invariably the heaviest component of a cooking setup for trips longer than a night or two. Plus youre not burning a fossil fuel, so that has green advocates on board. And they work very well, provided you have access to fairly dry fuel. You dont need a lot, twigs and pine cones work great, and some wood stoves will burn even damp materials.
In general, these stoves operate on the principle of a forge, with a small battery-operated fan that works as a bellows. That makes them very efficient and potentially very hot. One of the most popular commercially made wood stoves is the Sierra Stove ($57 for the basic version; www.zzstove.com). It uses a single AA battery for the fan and advertises six hours of battery lifeenough for five or six meals, or even more.
So that certainly competes well with liquid- or canister-fueled stoves. My take is, if they work (and they do), then why not? My caveats are: Weather could pose challenges on occasion, and in some areas fuel will be scarce (high, rocky areas), unavailable (high, snowy areas), or off-limits (national parks).
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