I am planning to hike for a week with two dogs. Each dog eats 4 cups of kibble a day, that's about 14 liters of kibble per week. The issue is the volume not the weight.
What can I feed them so that I do not have to carry so much?
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One problem is that dogs do not like changes in diet.
Search for calorie dense or weight gain dog food. I don't want to name brands. Work that into their diet before you leave.
Get packs for your dogs. But a nice dog pack is not cheap.
Fatten them up a bit before the trip.
When I was a kid we would fish and feed them a lot of fish. I get that is a change of diet but it is clean protein. Warning: even in a tent, a dog's fish fart is deadly.
There are a number of things you can do.
Use some puppy kibble with the adult dog food
Cut your dog food with about 25% puppy food during hiking trips. Puppy food had added calories and protein which will help boost your dogs nutritional intake during big mile days.
There is freeze dried dog food
Other than standard dog food, there are also several freeze-dried raw meat products on the market. This type of dog food is ideal for backpacking, either for people who feed raw, or for anyone wanting to supplement their dog’s trail diet, because of its small size and carrying weight. The only real downside is that it tends to be more expensive.
Use dog energy bars
Familiar with energy bars? Dog bars are a very similar concept. Each bar is formulated to work as either a meal replacement or meal supplement. Better yet, there are recipes made with ingredients to fuel up both you and your dog so that you can pack less. As we mentioned earlier, the most important thing to remember when choosing the type of bar you want to pack is the duration of your trip!
Do note that the dog will need more food than normal,
Your dog will need more calories than they normally eat if they are going to hike all day on the trail though. Dogs will need about 25% more calories than they normally eat to keep their energy up on a big adventure.
Beyond that, there are a number of articles and blog posts dealing with this that you might find useful.
Teach your dog to pack.
4 cups seems like a lot. Big dogs? Our dogs live outside in winter and get 2 cups. The two larger ones are 50-55 pounds. If the main ingredient in your dogfood is corn meal, and half the calories come out the back end. Many dogs do not digest corn meal well. Change brands. That alone may reduce the amount you have to carry.
Figure out a calories per cup for your food. Replace one quarter to one half the food with equivalent calories from fat. I would suggest using lard as it has less scent. You can melt these together to save volume. Fat runs about 3600 cal/pound, where cereals and proteins run about 14-1600.
Introduce this new diet to your dogs about a week ahead of time.
If the dogs aren't working hard enough not all the fat will be digested, and you will see greasy stools.
This is not a long term solution, as it is deficient in protein, and likely trace minerals.
If lower volume is sufficient, try mixing fish meal with fat. You may have to hunt for fish meal, but I've found it at any place that bulk sales ingredients for livestock and poultry feed. This will give you a compact brick. It will also reek.
You can make any food more efficient by adding water and cooking it. Dogs have fast digestive tracts and there are a lot of calories left in their crap. Cooking starts the breakdown process and pre-moistens the starches so that the dog gets more out of it. Cooking doesn't have to be complicated. Mix equal volumes dog food and water, and bring to a boil. Set aside for half an hour. When it's cool enough to eat, it's ready.