I've always felt the morning was better but then people bring up the other side of the equation where it takes less HP to run through the less dense afternoon air. I spent yesterday morning trying to figure this out and came up with the following and as I've mentioned before math isn't a strong point of mine.
First I used an often used formula that determines a cars drag force for a certain speed. It uses Cd, frontal area, air density and velocity desired to determine the drag force. I put in values that might be close to Hooley's Stude...... Cd of .40, frontal area of 24 sq. ft., 220 mph and 'standard' air densities for sea level, 4600 feet (morning) and 7200 feet (afternoon) and came up with the following:
..Altitude........Drag Force (lb/ft3)
.... 0 .............. 1152
.. 4600 ............ 974
.. 7200 ............ 882
From that we can see the drag force does change significantly with altitude and less dense air.
Next I took the Drag Force numbers and used them in a formula that determines HP needed to run a certain speed. This formula uses the Drag Force number along with the cars weight and rolling resistance to take that into account also. I used 6000 lbs for the weight and .20 for the rolling resistance and came up with the following HP numbers.
.. Altitude.........Drag Force...... HP Needed
.... 0 .................1152 .............. 732
..4600 ................ 974 .............. 628
..7200 ................ 882 .............. 574
From that we can see that the HP needed goes down as the air density goes down with altitude.
So the next question is how does the altitude effect the HP? Can we overcome the effects of altitude and less dense air by making more HP in the denser morning air.
I found a formula that calculates the loss of HP due to effects of altitude and less dense air. I started with 732 HP at sea level and then calculated what it would be at 4600 feet and 7200 feet and guess what?
.. Altitude ... HP
.... 0 ......... 732 Original HP
.. 4600 ...... 631 HP is down to this number at 4600 ft.
.. 7200 ...... 574 HP is down to this number at 7200 ft.
The conclusion I found using the formulas I found and used is that it is a wash. We loose HP at increasing altitude at the same rate that it is needed to run our 220 mph. We still run the 220 regardless of the altitude if we have the 732 HP needed to run it at sea level.
You need less HP at the higher afternoon density altitude but your HP will be down to the point that you could run in the morning with the same results as the HP gain there offsets the effects of the less dense air in the afternoon.
I guess this is a case where "air density" has the same weight or value in the equations to figure drag force and in HP loss.
Now there are other factors that could still come into play such as humidity. One thing to also consider is traction. It has been my feeling that traction is up in the morning and can go down in the afternoon as the heat brings water to the surface of the track. Also driver comfort...I'd much rather be running in the morning vs. the afternoon,
Sumner