I want to try this again. I had intended my first reply to be helpful; you obviously didn't see it that way. Perhaps this one will set things straight.
In my reply, I focused on your water planning. This is because water is the key to a safe and successful canyon hike. You will get the same story from the rangers. You can do the hike without food and without gear but not without adequate water. I had gotten the impression from reading your posts that you were planning on carrying no more than 1-2 liters from water source to water source; I thought that that was inadequate (still do) and suggested that you rethink your plans. BTW, I also think you need to cut your pack weight but others have already made a lot of good suggestions in this area. I will try to be a bit more specific about water in this post.
Were it me starting on the hike you propose I would first suggest that every member of your party carry one liter of water as an emergency reserve. More about this later. For water use on the trip: For the leg from the South Rim to BA carry one liter in addition to your reserve. Tank up at the rim, drink about a cup of water every 15 minutes on your way down, stop and tank up again at The Resthouse and at Indian Gardens and keep sipping at your 1 liter water bottle as you progress down the hill. For the next leg, from the river to Cottonwood, I would recommend starting with three liters after having drunk your fill at BA. Don't count on finding water between the river and CW; you might but don't count on it. For the final leg from CW to the North Rim, start the day with a gallon plus reserve and drink early and often. You will be mildly dehydrated by the time you get to the top but should still be functional. Tap your reserve when you are nearing the top. There are a few water sources on the CW to rim section.
The foregoing is based on the premise that you will keep on your projected time schedule. Don't assume that you will do so. You will be part of a party of six. In my experience, the odds favor something happening to at least one of you that will slow the party down. It could be a sore knee from the hike down, a case of plantar fasciitis, a case of the "green apple quickstep" or a bad headache. At any rate, in spite of an early start time you are likely to spend more time in the sun than you are planning. Also, you have two teenage males as part of your party. My experience in raising a few of these myself would suggest that an early start will be difficult. With my son, liberal use of a cattle prod was necessary to get him awake and going before sunup. Getting an early start is a good idea but your start and your progress may not be all you hope for. Unless you get a real early start, the climb from CW to the rim will be in the sun; you will be climbing a South-facing slope and once the sun comes up, it will get warm quickly. Also, the environment in which you will be hiking is a lot hotter than the recorded air temperature; you are dealing with heat radiated from the soil and hot air rising from a hot surface. I have measured temps of 120 at 3' above the surface where the air temp at 7' was 105.
This brings us to the water reserve. If a member of your party starts having difficulty with the heat, the water is used to help. Use some of the water to cool the person down; sponging and wet cloths will help treat incipient heat stress. If the person needs to be left behind while help is obtained, you can leave them with drinking water. And, the folks going for help may need extra water as well. Also, the reserve water will come in handy if a given leg of your trip takes longer than planned.
Your water reserve is basically a safety measure not to be used unless necessary. A lot of folks don't bother; I tend to be conservative about such things and others may not be. Use their advice and mine as you see fit.
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