Compensating for Density Altitude

Let me get this straight. When I calculate density altitude using the common private pilot formula....
What, exactly, is the "common private pilot formula"?

I was only taught the whiz wheel and the Koch chart.
 
I'm curious what most of you do to compensate for density altitude on those warm summer days at higher elevations. Is there much I should be doing beyond leaning and verifying my takeoff distance in the POH (with appropriate margin)? Would you have concerns taking off at max gross weight at a field with 7000' DA assuming the runway is "long enough"?

Wel aside from making sure the numbers work, you're going to have a little hotter engine on climb
 
Let me get this straight. When I calculate density altitude using the common private pilot formula, there's a significant discrepancy between the number I get and the number that ForeFlight gives, and that discrepancy proves not to be linear between airports, and asking about it here is in your view trolling.

Okey Doke.
How much is the discrepancy?
 
Rory McIlroy is that you???
 
Where I live (New York City), this time of year we have negative density altitudes.

I’d love to read any comments people have on that.
It's too freaking cold.
 
Wel aside from making sure the numbers work, you're going to have a little hotter engine on climb
That's an interesting point I had not thought of. What are the main reasons for that? Increased air temperature? Thinner air results in less cooling? The leaned mixture results in hotter combustion? All of the above?
 
Shouldn’t. Airspeed is airspeed. Unless you’re flying it at Vx or something, cooling should be the same.
That’s true. If the “pressure” into the pitot tube is the same, it would be the same on the airframe, or intake, or anything else.
 
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