It can't make over 75% power above 8000 anyway, so just leave the throttle wide open and lean until rough/enrich until smooth
Agreed. Why do you care if it's 55% or 65% power? The engine is fine at any setting up there. If you're worried about whether it can get up there for terrain clearance, stay at least 10% below max gross and give yourself at least 2000 feet margin during climb. Don't go with winds above 20 knots at the summit (whether stable or unstable). Cherokees (even with 180 HP) are very sluggish climbers above 10,000 feet.
It starts to be a strong function of temperature up there, as well.
By the way sorry for the orientation. Well lets say I want to go to 13,000ft at 2450 RPM does that round to 55% power? Do I just extend the lines and interpolate?
My "checkout" was a 2 hour round trip to Big Bear from Lancaster -- in a Warrior (it's possible, but you have to be aware of the limitations, especially how Vy is lower in IAS at 8000 feet than at sea level, and you DO NOT take off full rich). That's a minimum. There are all-day courses available that make landings on several high and eastern Sierra airports. That may be tough this time of year, as IMC (and ice) is common even when the weather is clear down below.
Read Sparky Imeson's book to start. There is a TON of good stuff in there.
And keep in mind that Lake Tahoe is well below 10,000 feet. Squawk Peak (the highest point around there) is just a bit above. Clearing Donner Pass or Echo Summit (which is slightly higher) with 2000 feet of clearance isn't too hard in Cherokee as long as the winds aren't high. Trying to get to Mammoth over Yosemite, with its 2000 AGL clearance (it's a national park) over a 10,000 foot pass, is another story. You won't get there at all on a warm day.
The main thing is, keep an out in case things don't go how you want.
I'd encourage you to contact a local flight instructor with signficant mountain experience. They aren't rare so near the Sierra, but they aren't every CFI either.
Cherokees (even with 180 HP) are very sluggish climbers above 10,000 feet.
Okay that right there I had a question about (Vy at altitude) I thought that Vy IAS will always be the same because you still need the same amount of pressure over the wings...but in writing this I realized you will have less power at altitude.
So how do you figure Vy at altitude then?
Cherokees (even with 180 HP) are very sluggish climbers above 10,000 feet.
And Arrows (Cherokee with folding gear) with 200 HP aren't any better, at least not on a warm summer day. BTDT.
That's where the tapered wing (Archer II, Arrow III/IV, etc.) helps -- a lot.
is running WOT at altitude bad of the engine?
Not just no, hell no. As long as the RPM is not over redline.
In many respects, flying at high altitude is like shortening the throttle knob (and lengthening the mixture).
If you have a manifold pressure gauge, there is usually a maximum MP for continuous operation. Above a certain altitude (it's like 5000 feet in a 182), full throttle won't exceed that. If your aircraft is turbocharged, that altitude might be high.