How much downforce?

Come spring and warmer garage temps I'll be starting the construction of my Challenge car. Until then I have all kinds of free time to think too much. Follow along and help me understand....

The car body is a 1973 TE27 Corolla so the plan view will be similar in size to NA/NB Miatas . The chassis will be rectangular tubing and set about 4" above ground. I can put the flooring above or below the chassis. If I were to put it below I can have a flat floor all the way from the front bumper to just ahead of the rear axle. So far as I can see nothing need protrude below that 4" plane all the way to the rear bumper. So, my question becomes is there merit in trying to construct a diffuser from the rear axle center line to the bumper and what would be a realistic expectation for down force?   OR ...would continuing the flat floor past the rear axle have any advantage?

Follow on question:  Even if it did generate down force, how much effect would it have on autocross times?

Edit: The flat floor area can be easily widened well beyond the rocker panels because the wheels and tires will protrude around 6" on each side. Would extra floor width matter if the ends are capped by 11" wide tires?

Well, let me try to answer in this order:

1. Downforce has a real effect on autox times. If you have a 2500 lb car that can corner at 1g with no downforce, that means the tires can provide 2500lb of lateral force. If you increase the push on the tires by 100lbs with downforce, that will increase the lateral force they are able to provide by close to 100lbs (but not quite 100, it would be less like 90 lbs). So then your car turns at 1.04g. with a lighter car or more downforce or less no downforce turning ability, the effect is magnified. Since your autox car should be near 100% turning capacity most of the run, this 4% advantage is carried most of the time. That adds up to a lot.

2. Maybe over-simply: Flat floors and diffusers work by speeding up the air under the car (like an airplane wing speeding up the air over the wing). This causes a pressure drop under the car, and the bottom of the car has a large surface area so you don't need much pressure drop to cause a big force. But if you have a pressure drop, air will start coming in from the sides too. So skirts can improve the effect significantly.

3. The diffuser is probably better than flat floor from rear axle back. I keep reading that 4-14 degrees is a good incline for the diffuser.

Let me add that when we say downforce, it's probably best to think in terms of "net". Ie the car probably makes quite a bit of lift in standard form. So reducing lift has the net effect of increasing downforce, even though there might still be actual lift.

In reply to Robbie :

I'll have to see if I can manage an inclined diffuser once I actually start welding up a chassis. I suspect the trunk area of a little car like this will get crowded pretty quickly.

DeadSkunk (Warren) said:

 

The car body is a 1973 TE27 Corolla so the plan view will be similar in size to NA/NB Miatas . The chassis will be rectangular tubing and set about 4" above ground. I can put the flooring above or below the chassis. If I were to put it below I can have a flat floor all the way from the front bumper to just ahead of the rear axle. So far as I can see nothing need protrude below that 4" plane all the way to the rear bumper.

Follow on question:  Even if it did generate down force, how much effect would it have on autocross times?

Edit: The flat floor area can be easily widened well beyond the rocker panels because the wheels and tires will protrude around 6" on each side. Would extra floor width matter if the ends are capped by 11" wide tires?

6" either side, miata-ish dimensions...

so, 66" nominal width, 78" max possible width;  89"-ish wheelbase, and 155" overall length?

In reply to sleepyhead the buffalo :

The Corolla shell is actually 5-6 inches narrower than a Miata, track width will be Miata plus whatever the 10" wide wheels add. Wheelbase will be 92-94" and overall length is whatever a stock '73 Corolla comes in at, probably without bumpers.

alright, so wiki has the following for the coupe

LOA: 155.3"
width: 59.3
wheelbase: 91.9"

this site has...
track width front: 49.4"
track width rear: 49.0"

and, if we target 60mph, which is 88 feet-per-second.

so, Downforce = 0.5*rho*(V^2)*S*Cl

and frequently, the part of "0.5*rho*V^2 is shortened to "q" as a stand in, since we sometimes compare different configurations at the same 'dynamic pressure'...

thus, the 'q' for this is....  0.5*.002377*(88^2) = 9.204 lb/ft^2

planform area comparisons is where things begin to get tricky.  I'm going to assume, just for the sake of convenience and time, that the overhangs are split between the front and back of the car.  That's probably not true, but it's a beginning.

and, lets guess that the oem corolla tires were 6" wide, so outside of the tires is ~55in, and between the tire is ~43".  Miata track width is ~56", so I'm going to add 4" of track per side for the 10" wheels (again, just to get somewhere)... which gives a max width of ~64"

so, nominal, 'flat floor, not including the wheels' of a '73 corolla is 155" x 43" = 6665sqin = 46.285sqft

if we add in just the width between the wheels (and, assume a ~25" tire diameter taken out of the wheelbase area)... so (91.9"-25")*(64"-43") = (67"*21") = 1407sqin = 9.771sqft

so you could have 56.056sqft if you add in flat floor between the wheels... or an additional 21% of available downforce area.

so, let's say you can make a Cl 0f 0.3 out of that flat floor...

then, OEM.area.downforce = 9.204 lb/sqft * 46.285 sqft * 0.3 = 127#s

and, Miata10".area.downforce = 9.204 lb/sqft * 56.056 sqft * 0.3 = 155#s

the next question to consider, is kind of twofold....

1) is 0.3 in the ballpark for a flat floor?
2) what kind of maximum 'lift coefficient' (or downforce coefficient if you prefer) can we generate from this floor?

In reply to sleepyhead the buffalo :

Not all that much down force, although I wouldn't expect a lot at 60 mph I guess. I'll have to do some more searching and see what I can learn. Really, the only additional work I'd have to do to the car would be the rear diffuser. A front splitter/floor will likely happen anyway, along with a trunk spoiler at minimum. Adding the diffuser would mean I'd have to try not to put things like fuel cell, Panhard bar and mufflers low behind the rear axle. I was already figuring the exhausts might exit just in front of the rear wheels, so the Panhard and cell are the only details to consider.