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Calculation of 99 spec downforce and lift.

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Old 09-19-16, 01:37 AM
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Calculation of 99 spec downforce and lift.

Can someone check my math? I'm terrible at actually using physics equations. But here's my attempt to calculate the downforce and lift of a stock 99 spec FD.


Here is the lift equation:
L = Cl * A * .5 * r * V^2
To find lift/downforce we need the coefficient of lift, the effective frontal area of the car (I think), air density, and speed.


Here are the coefficients of lift I used (from here: http://www.rx7.net.nz/newrx7.htm)

Rear wing @ 10 degrees (second highest setting):

Front lift coefficient .051 (net lift)
Rear lift coefficient -.058 (net downforce)

The CoD of the 99 spec is .31 and the front surface area is 1.79 m2, so it has an effective frontal area of 0.555 m2.

I assume air density of 1.225 kg/m3, which is a little high (15c at sea level). You then half this.

For speed, I did the calculations for 100 kph and 200 kph, which are roughly 27.8 and 55.6 m/s. You have to square these.


Multiplying everything together and you get about 15 kg at 100 kph and 60 kg at 200 kph in downforce at the rear.

At the front you get about 13 and 53 kg of lift at the same speeds. I bet lowering the front of the car a bit would greatly reduce this. It might increase downforce and at the rear, too.

At the the higher wing settings you'd get more rear downforce and front lift, and vice versa. At different speeds you'd get exponentially more or less downforce.

Did I do the calculations right? Keep in mind the actual data I used is off the internet.

Edit: I did the calculations for 300 km/h and got 137 kg, which is more than the R35 GT-R at the same speed, so obviously my calculations are circumspect. Although the GT-Rs rear wing is arguably less aggressive than the 99-spec's wing at it's 10 degree setting.

Last edited by Valkyrie; 09-19-16 at 05:15 AM.
Old 09-19-16, 07:39 PM
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AutoSpeed - Aero Testing - Part 5

Sounds about right compared to these numbers.

I thought it was cool Joseph Katz briefly mentions the FD in his book.

Ken
Old 09-20-16, 01:46 AM
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I do wonder why more rear downforce causes more front lift, though.

It is a little weird that the old stock spoiler (pre-99) didn't reduce lift. You'd think Mazda would notice.
Old 09-20-16, 02:22 AM
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Valkyrie


I do wonder why more rear downforce causes more front lift, though.

It is a little weird that the old stock spoiler (pre-99) didn't reduce lift. You'd think Mazda would notice.


-----------
Rear downforce causes front end lift because as the rear of the car is pushed down the front assumes a negative rake/angle of attack , so the front lip is less effective or even produces lift.
----------

Mazda purposefully made the old "wing" (or more precisely "floating spoiler" as Mazda called it) a zero downforce device because the FD had a high front end coefficient of lift they were trying to balance.

So they put a big front lip spoiler on to lower the front lift to equal the rear lift so the car's handling balance didn't shift with speed- at the cost of drag.

They called the rear "wing" a "floating spoiler" because it created turbulence both behind and below the "wing" to create a lower drag aerodynamic profile (longer tail).

This is all in the Yamaguchi book.
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Old 09-20-16, 03:11 PM
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After discussing the FD briefly, Joseph moves onto the Ferrari F355, which he denotes as the first production car to come out of the box with a full underbody panel. And as a result, it could be the first production car to actually have a negative lift coefficient (downforce). Underbody panel is really where you make your money as you are essentially turning your entire car into a spoiler as opposed to using spot treatment solutions such as front/rear spoilers.

I believe he was trying to paint a historical picture, where sports car design focus has moved from reducing drag coefficient to improving downforce coefficient.

Last edited by shineautoproject; 09-20-16 at 03:13 PM.
Old 09-20-16, 07:20 PM
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Originally Posted by shineautoproject
After discussing the FD briefly, Joseph moves onto the Ferrari F355, which he denotes as the first production car to come out of the box with a full underbody panel. And as a result, it could be the first production car to actually have a negative lift coefficient (downforce). Underbody panel is really where you make your money as you are essentially turning your entire car into a spoiler as opposed to using spot treatment solutions such as front/rear spoilers.

I believe he was trying to paint a historical picture, where sports car design focus has moved from reducing drag coefficient to improving downforce coefficient.
Tne FD has a relatively flat underbody as it is (at least until the rear submember), so there would probably be some gains from just closing off the center tunnel. That said, you'd need to cut holes or naca ducts into any panels you put down there to keep the transmission and exhaust from overheating. And unless you install a massive vent in the hood, you're still going to have to let a lot of the hot air flow under the car from the engine bay.

It would also make the car harder to service.

I am curious if off-the-shelf side skirts actually help generate negative pressure under the car.
Old 09-20-16, 07:25 PM
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Originally Posted by BLUE TII
[I]
-----------
Rear downforce causes front end lift because as the rear of the car is pushed down the front assumes a negative rake/angle of attack , so the front lip is less effective or even produces lift.
----------

Mazda purposefully made the old "wing" (or more precisely "floating spoiler" as Mazda called it) a zero downforce device because the FD had a high front end coefficient of lift they were trying to balance.

So they put a big front lip spoiler on to lower the front lift to equal the rear lift so the car's handling balance didn't shift with speed- at the cost of drag.

They called the rear "wing" a "floating spoiler" because it created turbulence both behind and below the "wing" to create a lower drag aerodynamic profile (longer tail).

This is all in the Yamaguchi book.
How does a spoiler that doesn't make any downforce balance the front?

What about the cars that didn't come with lips but still came with spoilers?

Does rear downforce physically (mechanically) take weight off the front tires, or does it just cause the front end to come up somehow without taking weight of the front tires, causing more air to flow under the chin?
Old 09-20-16, 09:58 PM
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How does a spoiler that doesn't make any downforce balance the front?

Joseph Katz book shows

Base model RX-7-
Lift Coefficient front= 0.16
Lift Coefficient rear= 0.08
Drag Coefficient= 0.29

R1 model RX-7-
Lift Coefficient front= 0.10
Lift Coefficient rear= 0.08
Drag Coefficient= 0.31

As you can see the front of the base FD body already had double the lift as the rear, so to balance the car Mazda decreased the front end lift on the performance model.

That way the increase in understeer with increase in speed would be minimal compared to the base FD body.

---------
What about the cars that didn't come with lips but still came with spoilers?

The non performance packages with the rear "wing" and no R1 front lip would have the same Lift Coefficients as the base FD body- at least at whatever speed the tests were done at above.

There is another published figure for the FD from the Yamaguchi book that shows-

Model of RX-7 not specified-
Lift Coefficient front= 0.01
Lift Coefficient rear= 0.04
Drag Coefficient= 0.31

Again, the speed is not specified. I would assume these figures are for the R1 model given the high drag and low front lift, but measured at a lower speed where there was less lift.
-----------

Does rear downforce physically (mechanically) take weight off the front tires, or does it just cause the front end to come up somehow without taking weight of the front tires, causing more air to flow under the chin?

Yes, both of those.

Some very small amount of weight is physically taken off the front with rear downforce if the downforce is generated behind the rear axle (the car pivots some on the rear wheels).

Mainly the effect is that because the rear is being pushed down the angle of attack (imagining the entire car body as the wing element) becomes positive (pointing upward at the leading edge).
Old 09-20-16, 10:39 PM
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Originally Posted by BLUE TII

Joseph Katz book shows

Base model RX-7-
Lift Coefficient front= 0.16
Lift Coefficient rear= 0.08
Drag Coefficient= 0.29

R1 model RX-7-
Lift Coefficient front= 0.10
Lift Coefficient rear= 0.08
Drag Coefficient= 0.31

As you can see the front of the base FD body already had double the lift as the rear, so to balance the car Mazda decreased the front end lift on the performance model.

That way the increase in understeer with increase in speed would be minimal compared to the base FD body.
That explains why they added a front lip, it doesn't explain why they added a rear spoiler that only generates drag.

---------
What about the cars that didn't come with lips but still came with spoilers?

The non performance packages with the rear "wing" and no R1 front lip would have the same Lift Coefficients as the base FD body- at least at whatever speed the tests were done at above.

[/quote]

....so what good is the wing?

There is another published figure for the FD from the Yamaguchi book that shows-

Model of RX-7 not specified-
Lift Coefficient front= 0.01
Lift Coefficient rear= 0.04
Drag Coefficient= 0.31

Again, the speed is not specified. I would assume these figures are for the R1 model given the high drag and low front lift, but measured at a lower speed where there was less lift.
-----------
You can insert your own speed into the lift formula and get actual lift/downforce, in theory. I'm just not sure if I'm using the formula the right way.

This is, of course, for the "zenki" (92-95) bumper and spoiler, I assume. The "chuuki" (96-98) wing is a little different, if memory serves, but has the same bumper and lip spoiler.


Yes, both of those.

Some very small amount of weight is physically taken off the front with rear downforce if the downforce is generated behind the rear axle (the car pivots some on the rear wheels).

Mainly the effect is that because the rear is being pushed down the angle of attack (imagining the entire car body as the wing element) becomes positive (pointing upward at the leading edge).
Ah! That makes sense. So it's like a see-saw, but you're only pressing down about a foot from the axle. By comparison the front of the car is so close to the front axle that it's not going to cause the rear to lift, and even if it did, it wouldn't significantly affect aerodynamics.

My car has a pretty aggressive body kit and splitter, but no rear wing, so I suspect my aero balance is pretty wacky.
Old 09-21-16, 01:11 AM
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Two things from my side of the fence- I have the genuine Mazdaspeed factory "15th Anniversary" body kit, which has a really low front lip and side skirts- I'd be interested to know if this kit was aerodynamically any better than the production car (being Mazdaspeed, you would think they would have thought it out fairly well, and its not just something for show).

The second thing is, I've got the 1996 era "whale tail" factory rear spoiler which is fixed, and doesn't particularly have any aggressive angle of attack or anything- its quite level and flat. I'd assume this thing only gives marginal (if any) rear downforce compared to the 99 spec rear spoiler which can have a high angle of attack.

I have an old book here- 'Race Car Engineering & Mechanics' by Paul Van Valkenburgh- its pretty thorough in its aerodynamics explanations. Might have to have another read of it again..
Old 09-21-16, 01:12 AM
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Because they needed the spiler to create turbulence, and thus reduce drag if i understand it correct.
Old 09-21-16, 06:28 AM
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Originally Posted by BLUE TII
Some very small amount of weight is physically taken off the front with rear downforce if the downforce is generated behind the rear axle (the car pivots some on the rear wheels).
It's not that small an effect. The longitudinal distance from the rear wing to the rear axles is about bout 25-30% of the wheelbase, so any downforce from a rear wing (or reduction in lift) translates into about 25-30% of that downforce as additional lift at the front wheels.

Mainly the effect is that because the rear is being pushed down the angle of attack (imagining the entire car body as the wing element) becomes positive (pointing upward at the leading edge).
This is also an effect, but added angle of attack will tend to add lift overall, not just at the front, whereas 100 lb. downforce from a rear wing directly translates into 125-130 lb. downforce at the rear wheels and 25-30 lb. lift at the front wheels.

Regarding the earlier R model car's rear spoiler apparently giving zero downforce, it's the same thing happening in reverse. The R's splitter reduced front Cl from 0.16 to 0.10. The reduction in lift at the front wheels is due to positive pressure pushing down on the splitter, which is well in front of front wheel centerline. This by itself would have increased lift on the rear wheels without the rear wing. Rear wing provides enough downforce to counter the rear lift from the splitter.
Old 09-21-16, 11:56 AM
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Quote:
Originally Posted by BLUE TII View Post
Some very small amount of weight is physically taken off the front with rear downforce if the downforce is generated behind the rear axle (the car pivots some on the rear wheels).


ZDan
It's not that small an effect. The longitudinal distance from the rear wing to the rear axles is about bout 25-30% of the wheelbase, so any downforce from a rear wing (or reduction in lift) translates into about 25-30% of that downforce as additional lift at the front wheels.


It is a very very small effect with stock spring rates and the stock aero.

When you put the weight on top of the wing while the car is on corner scales you will see that most the weight compresses the rear springs (and shows as rear weight increase) and barely any pivots off the rear wheels and takes weight off the front.

Well- I haven't exactly stacked weight on the stock wing, but I have put 120lbs of gasoline in the gas tank of the FD (behind the rear axle) and have seen the same effect on the corner scales.

If you have a wing that creates a lot of downforce and is far back on the car you will be running very high spring rates and the pivoting effect taking weight off the front is higher.
Old 09-21-16, 05:52 PM
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Originally Posted by Valkyrie
That explains why they added a front lip, it doesn't explain why they added a rear spoiler that only generates drag.
The R1 rear "spoiler" doesn't seem to have a traditional spoiler profile in the aerodynamic sense, so it is not producing any downforce. Very minimal, if any. Maybe if there was added kick towards the end of the spoiler it could create some downforce. The angle of the kick would need to be in between the sweet spot of 35-55 degrees. Any more or any less only produces drag. If someone can produce such an add-on, then it could be of some use.

The R1 spoiler seems to only be added for looks, only increasing weight and drag.
Old 09-21-16, 05:58 PM
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As ZDan mentions, neither the R1 front lip "spoiler" (which the Japanese tend to call them) or 99 Spec lip are spoiler designs either. They are more like splitters providing extra surface area in the front for higher air pressure to push down on. The other function is to help keep the front lower to the ground to help increase air velocity traveling under the car (if you can attach a flat undertray to the very bottom of the lip)... and also provide brake ducting in the case of the FD Rx7.

Last edited by shineautoproject; 09-21-16 at 06:00 PM.
Old 09-21-16, 06:17 PM
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Originally Posted by Valkyrie
Tne FD has a relatively flat underbody as it is (at least until the rear submember), so there would probably be some gains from just closing off the center tunnel. That said, you'd need to cut holes or naca ducts into any panels you put down there to keep the transmission and exhaust from overheating. And unless you install a massive vent in the hood, you're still going to have to let a lot of the hot air flow under the car from the engine bay.

It would also make the car harder to service.

I am curious if off-the-shelf side skirts actually help generate negative pressure under the car.
You are absolutely correct.

I haven't seen an OEM FD front underpanel or an OEM 99 spec front underpanel in some time. Was it relatively flat? OEM FD still needs a proper rear diffuser.

If one is to go full underpanel, strategic placement of naca ducts to cool things like the transmission, diff, etc is essential. Most full underpanel cars do have at least one naca duct, including the Ferrari F355 and the Lotus Exige.

Password JDM built a pretty nice full underpanel (front to rear diffuser) for the S2000.

http://passwordjdm.com/images/Products/2422_3.jpg

Something similar would suffice for the FD. Servicing would indeed be an issue. Voltex makes an extra long rear diffuser for the S2000, but shops hate servicing cars with them as you have to remove the rear diffuser every time.

For local "street class" track competition, often times a full underpanel is not allowed. Hence S2000 guys love the Voltex front bumper/lips w/ extended front undertray combined with the extended rear diffuser. It helps get the effect close to a full underpanel without actually having one. There are few tricks to get the air velocity to travel underneath the car quicker to mimic a full under panel system.
Old 09-21-16, 06:42 PM
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I have a 1999 Type RS and I can answer a couple of questions.

1. The 99 spec under tray is quite flat and weighs a lot less than the early spec one.

2. The adjustable wing makes a hug difference on track when angled at the 3 or 4 position (#1 being the default at the top). You do not notice any loss of traction from the front tires as you might need to be doing 120 mph or more in a corner to notice and I haven't been on any tracks with that cornering speed. What you do feel is a huge increase in grip in the rear, especially in mid to high speed corners as the car feels a bit loose in the rear with the wing at the #1 position in those situations. In fact you even notice it on the highway just cruising at 70-80 mph.

3. You can physically see it working by the amount of dirt on track the spoiler catches when tilted in the 3 or 4 position.
Calculation of 99 spec downforce and lift.-a8jt5md.jpg

Calculation of 99 spec downforce and lift.-bnqgard.jpg

Calculation of 99 spec downforce and lift.-fzsjhnp.jpg

Calculation of 99 spec downforce and lift.-jcpvsy9.jpg

Last edited by cib24; 09-21-16 at 06:44 PM.
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Old 09-21-16, 06:49 PM
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If I am correct, all modern Ferraris come right out of the box with a negative lift coefficient (downforce). All that is needed is to find ways to get air velocity traveling faster underneath the car vs. air velocity going above the car. Ferraris have employed a few tricks if one cares to observe their designs.

1. There is usually a raised inlet at the front of the bumper, which curves downward towards underpanel. This creates a Venturi effect at the very front helping to speed air velocity coming in. The more aggressive the curve, usually results in faster air velocity. But of course, they wouldn't design a bumper to have too aggressive of an opening or it would look unappealing. The only bumper I can currently think of that come close to mimicking this venturi effect is the FEED Type IIR front. And perhaps maybe a few RE-Amemiya variations.

2. Sometimes a few channels are added, similar to the Password JDM S2000 underpanel to help guide the air through its course, which is as straight as possible for the fastest air speed. This helps keeps the air "in place" during a cars lateral movements. Same principle behind fins on a rear diffuser, which existent in almost all modern Ferraris.

3. Aggressively curved rear diffuser. Ex. 599 XX. 430 Scuderia. 458 Speciale. All these special race edition Ferraris are making significantly more downforce than their less aggressive counterparts (599 GTB, Ferrari 430, 458 Italia) and that is mainly do to rear diffuser design along with a few minor changes in the front. The more aggressive the curve of the rear diffuser, the greater the velocity of air traveling underneath the car.



Valkyrie brought up the topic of sideskirts. I happen to believe sideskirts are one of the more underrated aerodynamic mods one can do to his car. Light weight, very low drag penalty (if designed properly), and very effective in keeping the low pressure air traveling underneath the car from mingling with the outside pressure creating a well balanced suction like downforce effect. Sideskirts were very effective in F1 Lotus' early 80's success and was shortly banned. However, the design of it matters and the more closed off (lower to the ground) you can achieve, the better. The problem is, for cars that are street driven, there needs to be clearance for speedbumps, potholes, dips, etc, so it is not ideal to drive around with sideskirts, which completely section off the air flow under the car. Ferraris, for the most part, do not have "sideskirts." They are more like side "panels" as the very low end only go as low as the underpanel, not lower to section off the air flow under the car. Many after-market sideskirts for the FD will suffice and have a similar effect. In my opinion, the lower the skirts, the better. Feed sideskirts would be a great design if it were 2 inches lower.

Front canards, depending on positioning, do help divert the air coming from the front of the car to help the effectiveness of a proper sideskirt.

Last edited by shineautoproject; 09-21-16 at 06:56 PM.
Old 09-21-16, 07:06 PM
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Originally Posted by cib24
I have a 1999 Type RS and I can answer a couple of questions.

1. The 99 spec under tray is quite flat and weighs a lot less than the early spec one.

2. The adjustable wing makes a hug difference on track when angled at the 3 or 4 position (#1 being the default at the top). You do not notice any loss of traction from the front tires as you might need to be doing 120 mph or more in a corner to notice and I haven't been on any tracks with that cornering speed. What you do feel is a huge increase in grip in the rear, especially in mid to high speed corners as the car feels a bit loose in the rear with the wing at the #1 position in those situations. In fact you even notice it on the highway just cruising at 70-80 mph.

Thanks you for sharing. If you had to guestimate the angle in degrees of position 3 & 4, what would you guess it at?

Ken
Old 09-21-16, 07:27 PM
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The 99 spec changes and wing details can be found here:

'99 FD3S

Calculation of 99 spec downforce and lift.-deserih.jpg
Old 09-21-16, 07:36 PM
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It should be pointed out that a 0.075 increase in downforce only causes a 0.008 increase in front lift, which is pretty insignificant by comparison. It shouldn't cause too much understeer while settling the rear. I'm sure the CD is higher than .31 at the maximum setting though.
Old 09-21-16, 07:40 PM
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Originally Posted by cib24
The 99 spec changes and wing details can be found here:

'99 FD3S

Ah. Good find. The picture seems to be giving adjustment in degrees from pivot point of the wing.

My question is more along the lines of, what is the angle of attack relative to the flat trunk of the FD? It certainly looks more aggressive than 14 degrees.

Ken
Old 09-21-16, 07:46 PM
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Also worth noting from the link on 99 spec changes:

Big front lip.
"On the old FD a front lip air dam was fitted to the Type R and available on other models as an option.
Due to the huge openings in the front of the New FD, the volume of air entering at speed could not pass through the radiator fast enough and was coming back out again. This excess air was then flowing under the car, reducing the negative pressure and unsticking the car from the road. To combat this problem a much larger lip was added to the bottom of the front spoiler and extended to carry any excess air around to the sides of the car.
The lip also extends further forward and collects air from the in front of the car, further reducing the pressure under the car, increasing down force."
Old 09-21-16, 07:50 PM
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Originally Posted by shineautoproject
Ah. Good find. The picture seems to be giving adjustment in degrees from pivot point of the wing.

My question is more along the lines of, what is the angle of attack relative to the flat trunk of the FD? It certainly looks more aggressive than 14 degrees.

Ken
Not sure. I can try to measure it if I get a hold of a protractor. Passed geometry ages ago when I was a kid so don't have one of those on hand ;-)
Old 09-21-16, 07:54 PM
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Originally Posted by Valkyrie
It should be pointed out that a 0.075 increase in downforce only causes a 0.008 increase in front lift, which is pretty insignificant by comparison. It shouldn't cause too much understeer while settling the rear. I'm sure the CD is higher than .31 at the maximum setting though.
There is an interesting graph in Joseph Katz' book (towards the end of the book), Designing for Speed, which discusses rear spoiler angle of attack in relation to drag. There is actually a sweet spot which only marginally increases drag. Beyond that sweet spot, drag increases almost exponentially (without any downforce benefits), which is why I inquired what the angle of attack was.

I lost my book years ago lol. If I can find one at the book store, I'll snap a pic of that page.

For whatever it's worth, the impression I got from Katz is...the more downforce, the better (for a track car), even if it comes at the expense of increasing drag.


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