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Hello, and welcome to another DataHunter Transmission Mystery Thread. For those of you unfamiliar with these sorts of things, have a look at the following: Requesting Information on the Bugatti EB110
Today, I hope I can bring the community together to tackle a smaller (albeit still pretty neat) mystery - this time, the Porsche 918's PDK transmission will be subject to our collective scrutiny. The issue concerns a mysterious discrepancy I noticed while examining the 918's geared speeds - in fact, so great is this discrepancy that (depending on the source) the top speed in first gear is different by a whopping 30 km/h!
Let's take a look at what I'm talking about. For the purposes of brevity, we'll use first gear as our reference point. In general, the top speed of the 918 in first gear is either reported as
a) 75-ish km/h
Auto (Italy)
scans credit: Dede
AutoZeitung
scans credit: Dede
Quattroruote
scans credit: Dede
b) 105-ish km/h
Autocar
scans credit: Switar (OFFICIAL - Porsche 918 Spyder)
Road and Track
scans credit: EKaru @ m3forum.net (Redirect Notice)
So what gives? Well... it becomes readily apparent if you take a closer look at the way each magazine reports its geared speeds. Road and Track comes right out with it: in the 105 km/h camp, the geared speeds are calculated. It would appear that 75 km/h is the measured top speed of the 918 in first gear, and thus - the true top speed of the 918 in first gear.
Why is there such a difference, then? Real world numbers are usually a little different than their theoretical counterparts (due to tire slip, centrifugal expansion, the load on the tire, transmission error, etc.), but not by that much. Are English-speaking magazines just really terrible at math, then?
Not really. You can try it yourself, using the information provided by Porsche themselves (http://press.porsche.com/vehicles/2015/Tech-Specs-2015-Porsche-918-Spyder.pdf).
Step 1. The 918's first gear ratio is quoted as (to three significant figures) 3.91:1, and its final drive ratio is given as 3.09:1 (again, with only three significant figures). This gives a total overall reduction ratio of 3.91:1 x 3.09:1 = 12.1:1*
Step 2. The tire size used on the 918's rear wheels are given as 325/30R21. A quick search of tirerack.com yields this same tire, an original equipment (OEM) Michelin Pilot Sport Cup 2 (Michelin Pilot Sport Cup 2 for 2015 Porsche 918 Spyder). Specs on the tire give a free rolling radius of 724 revolutions per mile (for the sake of simplicity, we will ignore tire slip and assume the 918 is coasting). The tire's free rolling radius can be computed as
(5280 ft. per 1 mi.)x(0.3048 m per ft.) / ((724 rev. per mi.)x(2π radius per rev.)) = 0.354 m radius
Step 3. As the 918 is often quoted as having a fuel cutoff of 9150 rpm, we can calculate the same geared speed for first gear. The calculation is as follows.
(9150 rev. per min.)x(60 min. per hour)x(0.354 m rad.)x(2π rad. per rev.)/((1000 m per km)x12.1) = 101 km/h.
This is very nearly what you might expect from Autocar and Road and Track. But then why do other magazines quote 75 km/h? The answer lies in the way Porsche presents its information: they forget to include the constant gear ratio when reporting the 918's final drive ratio.
What is the constant gear ratio? To put it simply, the ZF 7DT transmission (A.K.A. the Porsche PDK) uses a gear reduction before the bevel pinion gear (as seen in this diagram):
The constant gear pair is seen in the diagram, labeled "Constants". The 911R uses a constant gear ratio of 1.216:1, for example (http://press.porsche.com/newyorkautoshow2016/pdf/2016_911_R_Technical_Specifications.pdf). Indeed, the 3.09:1 ratio quoted for the final drive is really the 34:11 hypoid ring and pinion used in virtually all ZF 7DT transmissions.
A constant gear which makes sense for the geared speed data should be about 1.4:1, although it is impossible to say with any degree of accuracy. So I posit this question: what is the Porsche 918's constant gear ratio? Can anyone provide sources which might tell us the answer?
I'd like to contact Porsche themselves, but unless you live in Germany, Romania, Italy, China or the Czech Republic - you cannot contact Porsche Engineering to set the record straight.
Today, I hope I can bring the community together to tackle a smaller (albeit still pretty neat) mystery - this time, the Porsche 918's PDK transmission will be subject to our collective scrutiny. The issue concerns a mysterious discrepancy I noticed while examining the 918's geared speeds - in fact, so great is this discrepancy that (depending on the source) the top speed in first gear is different by a whopping 30 km/h!
Let's take a look at what I'm talking about. For the purposes of brevity, we'll use first gear as our reference point. In general, the top speed of the 918 in first gear is either reported as
a) 75-ish km/h
Auto (Italy)
scans credit: Dede
AutoZeitung
scans credit: Dede
Quattroruote
scans credit: Dede
b) 105-ish km/h
Autocar
scans credit: Switar (OFFICIAL - Porsche 918 Spyder)
Road and Track
scans credit: EKaru @ m3forum.net (Redirect Notice)
So what gives? Well... it becomes readily apparent if you take a closer look at the way each magazine reports its geared speeds. Road and Track comes right out with it: in the 105 km/h camp, the geared speeds are calculated. It would appear that 75 km/h is the measured top speed of the 918 in first gear, and thus - the true top speed of the 918 in first gear.
Why is there such a difference, then? Real world numbers are usually a little different than their theoretical counterparts (due to tire slip, centrifugal expansion, the load on the tire, transmission error, etc.), but not by that much. Are English-speaking magazines just really terrible at math, then?
Not really. You can try it yourself, using the information provided by Porsche themselves (http://press.porsche.com/vehicles/2015/Tech-Specs-2015-Porsche-918-Spyder.pdf).
Step 1. The 918's first gear ratio is quoted as (to three significant figures) 3.91:1, and its final drive ratio is given as 3.09:1 (again, with only three significant figures). This gives a total overall reduction ratio of 3.91:1 x 3.09:1 = 12.1:1*
Step 2. The tire size used on the 918's rear wheels are given as 325/30R21. A quick search of tirerack.com yields this same tire, an original equipment (OEM) Michelin Pilot Sport Cup 2 (Michelin Pilot Sport Cup 2 for 2015 Porsche 918 Spyder). Specs on the tire give a free rolling radius of 724 revolutions per mile (for the sake of simplicity, we will ignore tire slip and assume the 918 is coasting). The tire's free rolling radius can be computed as
(5280 ft. per 1 mi.)x(0.3048 m per ft.) / ((724 rev. per mi.)x(2π radius per rev.)) = 0.354 m radius
Step 3. As the 918 is often quoted as having a fuel cutoff of 9150 rpm, we can calculate the same geared speed for first gear. The calculation is as follows.
(9150 rev. per min.)x(60 min. per hour)x(0.354 m rad.)x(2π rad. per rev.)/((1000 m per km)x12.1) = 101 km/h.
This is very nearly what you might expect from Autocar and Road and Track. But then why do other magazines quote 75 km/h? The answer lies in the way Porsche presents its information: they forget to include the constant gear ratio when reporting the 918's final drive ratio.
What is the constant gear ratio? To put it simply, the ZF 7DT transmission (A.K.A. the Porsche PDK) uses a gear reduction before the bevel pinion gear (as seen in this diagram):
The constant gear pair is seen in the diagram, labeled "Constants". The 911R uses a constant gear ratio of 1.216:1, for example (http://press.porsche.com/newyorkautoshow2016/pdf/2016_911_R_Technical_Specifications.pdf). Indeed, the 3.09:1 ratio quoted for the final drive is really the 34:11 hypoid ring and pinion used in virtually all ZF 7DT transmissions.
A constant gear which makes sense for the geared speed data should be about 1.4:1, although it is impossible to say with any degree of accuracy. So I posit this question: what is the Porsche 918's constant gear ratio? Can anyone provide sources which might tell us the answer?
I'd like to contact Porsche themselves, but unless you live in Germany, Romania, Italy, China or the Czech Republic - you cannot contact Porsche Engineering to set the record straight.
