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The same way one would apply the brake and accelerator, the more torque the more break is needed to hold the car, can a plane use this same technique to check the plane thrust and air density before take off?
Using a brake pressure gauge, could density altitude be measured by how much pressure is needed to hold the plane in place?
You may be able to get a rough estimate of if your engine is producing sufficient thrust utilizing brake pressure. But, how will you determine how much thrust is being produced? Your brakes are not calibrated so carefully as to adequately determine that. You would only be guessing. You might get a better indication of engine performance by utilizing the sound of the engine.
The best way to tell if your engine is producing enough power with a fixed pitch prop is using your tachometer. One is required for all flight in a powered civil aircraft with a standard category U.S. airworthiness certificate in the US by 14 CFR 91.205. With a constant speed prop, you are required to have a manifold pressure gauge to indicate the power output of the engine.
On the other hand, even if you could judge your engine output without instruments, it still would not account for the effect of density altitude on the lift producing airfoils. Instead, you are better off determining density altitude using the weather data that you should have reviewed during your preflight planning required by 14 CFR 91.103. For that, you need no aircraft instruments.
You would have to have a brake pressure indicator that shows the pressure being applied to the calipers, where you could observe the minimum pressure required to hold the plane when WOT, and some charts or calculations that showed the static thrust being produced with a given amount of brake pressure. But then the amount of pressure varies with a lot of things, how wet they are, how worn they are etc. etc. An awful lot of scatter.
If you really wanted to do that sort of thing, the most practical thing to do with a reliable amount of precision would be to carry along a force gauge (digital fish scale more or less) with a bit of rope and tie the plane to a fence post with the force gauge and do a brief full power run and measure your static thrust directly, then interpolate performance based on that.
I don't know of anybody that's ever done that, ever. Why bother when the manufacturer has already tested all the permutations and conditions and produced performance charts, and all you need to do is plug in the numbers on the charts and follow the little lines to get reliable, conservative values.
