**Exclusive to RotaryNews.com**
by Edwin Krampitz, Jr. (ekrampitzjr)
Mazda has been coy about what the 16X rotor dimensions will be. Based on a bunch of detective work from the Mazda website and a recent US patent application, along with a lot of algebra and number crunching, I believe I have determined them:
Rotor radius (R) = 120 mm
Equidistance (a) = 2 mm
R' (R-prime) = R + a = 122 mm
Rotor eccentricity (e) = 18 mm
Rotor width (B or W) = 70 mm
K ratio = R/e = 6.67:1 (using R, not R')
Displacement using R' as Mazda (technically incorrectly) does:
798.8 cc/rotor, 1598 cc/engine
Major axis = 280 mm; minor axis = 208 mm
My confidence in the accuracy of these dimensions is very high, based on information in the patent application in particular. Read on for the technical details explaining how I determined these numbers....
Mazda first displayed prototypes of the new direct-injection 16X rotary in 2007, which will see use in upcoming vehicles and has appeared in recent show cars, but Mazda has so far been coy about its rotor dimensions. I believe I have deduced them; here I present my logic. This is a little long, so bear with me.
We know that the 16X uses a new trochoid with greater rotor radius (R) and eccentricity (e) than those of the 10A/12A/13B/RENESIS family, and its rotor width (B or W) is narrower than that of the 13B/RENESIS. In particular, e is larger for better low-speed torque. The stated displacement is 1600 cm³ (800 cm³/rotor), nearly 300 cm³ larger than that of the 13B/RENESIS, but Mazda has not given specific values for R, e, B, or the trochoid equidistance a, which (roughly speaking) is the allowance for the rotor apex seals.
For public consumption Mazda usually gives R’ (R-prime), or R + a, instead of R, and—though technically not correct—uses R’ in displacement calculations. The reason Mazda uses R’ seems to be that it has always been 105 mm in the 10A/12A/13B family, though R and a individually have changed over 40 years of rotary engine production. Lower values of a are better for technical reasons, and R and a in this engine family went from 101/4 mm until 1973 to 102/3 mm until 1986 to 103/2 mm since 1986.
Here are those figures for the RENESIS:
R = 103 mm
a = 2 mm
R’ = R + a = 105 mm
e = 15 mm
B = 80 mm
K ratio = R/e = 6.87:1 (not using R’)
Displacement using R’ as Mazda does:
654.7 cm³/rotor, 1308 cm³/engine
Mazda has given some clues to the 16X dimensions, both in its online publicity and in a new US patent application, US 20090101103, filed in April 2009. The title of the application is “Rotary piston engine and method for designing the same”, inventors Shimizu and Ueki, assignee Mazda.
To simplify this complex issue a lot: important new in-house combustion research showed that the rotor width B needed reduction for greater efficiency, especially for power generation, but also for improved fuel economy. By treating the face of the rotor as a rectangle, Mazda determined that B should be 76 mm maximum, and 70 mm is even better. Otherwise the burning charge does not reach the full width B, wasting fuel—and note that B for RENESIS exceeds this dimension and a common RX-8 complaint is poor fuel economy.
In a table the patent application gives different dimensions studied for the length of the rectangle, which would be the linear distance from apex to apex including its slight convexity (bulging out in the center). One of these, 182 mm, is clearly that for the RENESIS; two others studied were 208 mm and 222 mm.
On its website Mazda shows an outline of the RENESIS trochoid within a picture of the 16X, which allowed a rough-and-ready measure from the computer screen. The major axis is 2R’ + 2e, so for the RENESIS it is 240 mm (2 × 105 + 2 × 15). Proportionally the 16X major axis comes out to about 280 mm.
Let’s treat the rotor as an equilateral triangle. We know the approximate length of one side from the table in the patent application. We want the rotor radius, which is the distance from the center of the rotor to the apex, so the analogue for the triangle is center to point. This is the same thing as the radius of a circumscribed circle. The formula R = side × tan 30° = side × 0.5774. To check how accurate this is for RENESIS, R is known to be 105 mm and S given in the patent application is 182 mm. 182 × 0.5774 = 105.1 (rounded), so the formula works well and we can ignore the rotor face convexity.
For the new designs investigated in the patent application, S = 208 and 222. The formula gives R of 120 mm and 128.2 mm. The higher figure is unlikely. We know that B will certainly be no more than 76 mm and will be more likely 70 mm at most. The equidistance a has been 2 mm for over 20 years and seems unlikely to change now. It’s logical to figure that the displacement won’t be exactly 1600 cm³, but a little under. It’s also logical to figure that a will change proportionally more than R to improve torque, so the K ratio will be lower.
These points, some algebra, and a bit of number crunching give me the following dimensions for the 16X:
R = 120 mm
a = 2 mm
R’ = R + e = 122 mm
e = 18 mm
B = 70 mm
K = R/e = 6.67:1 (not using R’)
Displacement using R’ as Mazda does:
798.8 cm³/rotor, 1598 cm³/engine
The major axis is 280 mm—in agreement with the proportions measured from the computer screen. The minor axis is 208 mm.
In 2007 a Japanese fan site took a stab in the dark at the rotor dimensions. Its guess was very close, giving R (actually R’) as 122.5 mm and e as 17.5 mm, and agreeing with me for B as 70 mm. Its computations resulted in a rotor displacement of 797 cm³, very close to my deduction. However, my work is clearly not based on that guess.
Hope this helps all you rotorheads. |