Secrets of the Simpson Gearset


By the late seventies, the limitations of three-speed automatics were already becoming apparent. With an axle ratio tall enough to provide relaxed, economical cruising, smaller emission-controlled engines needed wide-ratio gearsets for decent off-the-line punch, which left painful gaps between the ratios and made it harder to keep the torque converter locked up for better fuel efficiency. Compromise gearing often made for an unhappy combination of lackluster acceleration, sub-par fuel economy, and irritatingly buzzy highway rpm.

The immediate solution, other than to stick with a manual gearbox, was automatic transmissions with an overdrive top gear. Overdrive allowed a shorter axle ratio for better acceleration while still keeping cruising rpm lower than would generally be practical with a three-speed automatic.

Many four-speed overdrive automatics were essentially revisions of existing three-speed units. Some obtained the additional ratio by rearranging how the existing elements interconnected; Ford’s four-speed AOD transmission, which we’ve described elsewhere, was a revamp of the Ravigneaux gearset MX/FMX transmissions. Others, like the GM 200-R4 and the ZF 4HP22, were Simpson gearset automatics with an additional planetary gearset to provide an overdrive ratio after the the shift to the direct drive third gear.

Although three-speed automatics remained common throughout the eighties and persisted on some inexpensive models into the 21st century, four-speeds became the norm by the early nineties. These eventually gave way to automatics with five or more speeds. Some of these later multi-speed transmissions still retained some recognizable elements of older Simpson gearset designs, although calling them that strains the definition.

Color diagram of Howard Simpson's 12-speed tractor transmission © 2017 Aaron Severson

The transmission illustrated in this diagram is not a Simpson gearset, but it IS a gear train designed by Howard Simpson. Intended for tractors, this dual-planetary layout provided eight speeds forward and four reverse gears. (author diagram)

However, in this regard, Simpson himself was ahead of the curve. Back in 1959, he designed a dual-planetary transmission using three brakes and six clutches to provide eight forward speeds, including direct drive and two overdrive ratios. (A patent was granted for this design in May 1962, U.S. Patent No. 3,031,901.) Simpson intended this transmission for tractor duty — as evidenced by the four reverse gears — but with today’s proliferation of eight-, nine-, and even 10-speed passenger car automatics, it looks surprisingly prescient.


I’d like to make a special shout-out to Matthias Wandel’s website. In writing both this article and the earlier split torque article, I looked at a lot of different references to try to get my head around how to calculate planetary gearset ratios. Although not specifically about automotive transmissions, Wandel’s straightforward explanation was enormously helpful for your math-challenged author to grasp the basic principles well enough to extrapolate them to different situations. (For the record, I have no affiliation with that site and have never spoken with Wandel; I merely found his published work very helpful!)


Our sources on Howard Simpson and his designs included R. August, R. Kasuba, J.L. Frater, and A. Pintz, “Dynamics of Planetary Gear Trains,” NASA Contractor Report 3793 (Grant NAG3-186), June 1984; Cernil Bagci, “Efficient Methods for the Synthesis of Compound Planetary Differential Gear Trains for Multiple Speed Ratio Generation,” Gear Technology July/August 1990: 14–35; John Barach, “Cadillac History,” Motor Era, n.d., www.motorera. com/ cadillac/index.htm, last accessed 21 October 2017; Roy Beardmore, “Epicyclic Gears,” Roymech, 20 January 2013, www.roymech. Epi_cyclic_gears.html, accessed 20 August 2017; Ford R. Bryan, Henry’s Lieutenants (Chicago: Wayne State University Press: 1993); Joseph M. Callahan, “Design of Dying Engineer Sweeping Auto Industry,” Automotive News 6 July 1964; Bert W. Cartwright, Teno Iavelli, and Ervin R. Miller, assignors to Chrysler Corporation, U.S. Patent No. 2,932,990A, “Transmission,” filed 14 October 1954, issued 19 April 1960; Charlie Tranny, “C6,” n.d., www.charlietranny. com/ c6.htm, 2 October 2017, and “Ford C4 transmission,” n.d., www.charlietranny. com/ c4.htm, accessed 2 October 2017; Chrysler Division, Chrysler Corporation, “Imperial” [brochure CS-375], September 1956; “Chrysler’s TorqueFlite automatic transmission,”, n.d., www.allpar. com, accessed 17 October 2017; David E. Davis, Jr., “Chrysler Imperial,” Car and Driver Vol. 26, No. 7 (January 1981): 69–75; Kevin Elliott, “Automatic for the People,” Hot Rod 14 September 2009, www.hotrod. com/ articles/ 0911rc-ford-automatic-transmission/, accessed 2 October 2017; Ford Division of Ford Motor Company, “The New Ford Mustang” [press kit], April 1964; Michael Galimi, “Ford C6 Transmission Upgrades – Built Tough,” Modified Mustangs & Fords 7 February 2012, www.mustangandfords. com/ how-to/ drivetrain/ mdmp-1203-ford-c6-transmission-upgrades/, accessed 2 October 2017; Philip G. Gott, Changing Gears: The Development of the Automotive Transmission (SAE Historical Series) (Warrendale, PA: Society of American Engineers, 1991); T. Grace, Automatic Transmission Service Guide (Union, NJ: Lincoln Technical Institute, September 1966); Tom Hand, “The TorqueFlite Automatic Transmission,” WPC News Vol. 15, No. 5 (January 1984): 4–22; Ari Holopainen, “Planetary Gears,” LUGNET News, 2005, www.lugnet. com/~3813/epicyclic, accessed 4 September 2017; Roger Huntington, “The Great Transmission Controversy: Coupling vs. Converter,” Car Life Vol. 10, No. 2 (March 1963): 18–21; Jim Kaekel, Jr., “GM TH-200: From the Court Room to the Race Track,” Motor State Distributing, May-June 2013, www.motorstate. com/GMTH-200.htm, accessed 2 October 2017; Alexander L. Kapelevich, “Analysis and Optimization of Asymmetric Epicyclic Gears,” Gear Solutions Vol. 61, No. 7 (August 2016): 50–55; Claus-Peter Köth, “50 Jahre Automatgetriebe von ZF,” Automobil Industrie, 5 August 2015, www.automobil-industrie.vogel. de, accessed 21 October 2017; Michael Lamm, “Driving the 1980 Dodge, Plymouth, and Chrysler Models,” Popular Mechanics Vol. 152, No. 4 (October 1979): 102–103, 246–248; “Man with a Pencil: Engineering Genius of the Modern Automatic Transmission,” Motor Trend Vol. 16, No. 10 (October 1964): 82–85; Le Roy F. Maurer, assignor to Automatic Turbine Drive Company, Inc., U.S. Patent No. 2,329,724, “Transmission,” filed 7 December 1937, granted 21 September 1943; Karim Nice, “How Gears Work,”, 16 November 2000 science.howstuffworks. com/ transport/ engines-equipment/gear.htm, accessed 11 August 2016; the Old Car Brochures website (; Nissan Motor Co.., Ltd., Export Engineering Dept., Service Manual: Nissan Full Automatic Transmission Model 3N71A (Publication No. 29811), ca. 1972; the Old Car Manual Project (; the Online Imperial Club website (; George Reid, “How to Assemble Ford C4 Transmissions: Cruise-O-Matic / Select Shift,” DIY Ford, n.d., assemble-ford-c4-transmissions-cruise-o-matic-select-shift/, accessed 2 October 2017, and “How to Build a Ford C6 Select Shift Transmission: Step by Step,” DIY Ford, n.d., www.diyford. com/ build-ford-c6-select-shift-transmission-step-step/, accessed 2 October 2017; Rick O. Rittenberg, Challenger and Barracuda Powertrain Databook (Totowa, NJ: Lightning Press, 2021); Howard W. Simpson, assignor to Ford Motor Company, U.S. Patent No. 1,488,136A, “Fender and Safeguard for Tractors,” filed 7 November 1921, granted 25 March 1924; U.S. Patent No. 1,875,767A, “Tractor Pulley,” filed 8 September 1930, granted 6 September 1932; U.S. Patent No. 1,963,686A, “Tractor Wheel Spade,” filed 10 June 1931, granted 19 June 1934; U.S. Patent No. 2,088,782A, “Transmission,” filed 28 September 1935, granted 3 August 1937; U.S. Patent No. 2,132,728A, “Transmission,” filed 2 January 1936, granted 11 October 1938; U.S. Patent No. 2,177,951A, “Transmission,” filed 24 February 1936, granted 31 October 1939; Howard W. Simpson, “Discussions: Finds TorqueFlite Design Gives Satisfactory Performance,” SAE Transactions Vol. 66 (1958): 165; U.S. Patent No. 2,518,824A, “Transmission,” filed 16 September 1944, granted 15 August 1950; U.S. Patent No. 2,518,825A, “Transmission,” filed 27 June 1946, granted 15 August 1950; U.S. Patent No. 2,749,773A, “Hydrodynamically Driven Planetary Transmission,” filed 15 December 1951, granted 12 June 1956; U.S. Patent No. 2,749,775A, “Planetary Transmission for Self-Propelled Vehicle,” filed 27 December 1951, granted 12 June 1956; U.S. Patent No. 2,749,777A, “Planetary Transmission for Self-Propelled Vehicle,” filed 15 December 1951, granted 12 June 1956; U.S. Patent No. 2,786,369A, “Planetary Transmission,” filed 6 February 1953, granted 26 March 1957; U.S. Patent No. 2,826,936A, “Variable Speed Transmission,” filed 3 August 1953, granted 18 March 1958; U.S. Patent No. 2,856,794A, “Planetary Transmission for Self-Propelled Vehicle,” filed 13 December 1955, granted 21 October 1958; U.S. Patent No. 2,856,795A, “Planetary Transmission for Self-Propelled Vehicle,” filed 11 June 1956, granted 21 October 1958; U.S. Patent No. 2,873,625A, “Planetary Transmission for Self-Propelled Vehicles,” filed 4 April 1957, granted 17 February 1959; U.S. Patent No. 3,031,901A, “Twelve Speed Power Shift Planetary Transmission,” filed 23 September 1959, granted 1 May 1962; and U.S. Patent No. 3,319,491A, “Heavy Duty Planetary Transmission,” filed 24 December 1963, granted 16 May 1967; Howard W. Simpson, assigner of one-third to General Motors Corporation, U.S. Patent No. 2,914,967A, “Planetary Transmission,” filed 20 August 1956, granted 1 December 1959; Jim Smart, “How to Build a Better C4 Transmission,” Modified Mustangs and Fords, 1 August 2009, www.mustangandfords. com/how-to/ drivetrain/ mdmp-0404-ford-automatic-transmission-c4/, accessed 2 October 2017; “Test Update: The Cat Strikes Back,” Autocar 7 October 1987, reprinted in Jaguar XJS Gold Portfolio 1975–1988, ed. R.M. Clarke (Cobham, Surrey: Brooklands Books Ltd., ca 1989): 147–149; William K. Toboldt and Larry Johnson, Goodheart-Willcox Automotive Encyclopedia (South Holland, IL: The Goodheart-Willcox Company, Inc., 1975); “Transmission Gearing Ratios,” TCI Automotive, n.d., www.tciauto. com/tc/ gear-ratios/, accessed 2 October 2017; Matthias Wandel, “Planetary gear ratio calculations,” Woodgears, gear/ planetary.html, last accessed 12 October 2017; and ZF AG, “50 Years of Automatic Transmissions,”, 5 July 2015, www.zf. com/corporate/en_de/ magazine/magazin_artikel_viewpage_22099816.html, accessed 22 October 2017.

The typeface used in this article’s author-created diagrams and other graphics is Liberation Sans, one of the Liberation Fonts (version 2.00.1 or later), which are copyright © 2012 Red Hat, Inc., used under the SIL Open Font License, Version 1.1. Liberation is a trademark of Red Hat, Inc. registered in U.S. Patent and Trademark Office and certain other jurisdictions. Red Hat is a trademark of Red Hat, Inc., registered in the United States and other countries.



Add a Comment
  1. Thank you for continuing this fascinating exploration of the technical details and history of automatic and semi-automatic transmissions. I’ve been interested in cars since 1985 when I was finally within reach of driver’s license age and I have read quite a bit of the engineering history of the automobile but I still had no idea of the variety of designs that the American manufacturers put on the road before getting to what I always thought of as the norm – three speed plus reverse, torque converter coupled automatic with the PRND21 shift pattern. I had read references to “slip and slide with Powerglide” but the only car I ever drove with an automatic that was different from the C4/C6/Turbo-Hydramatic/Torquflite experience was a VW Beetle with the semi-automatic transmission. I hope you do an article on pre-selectors someday too.

    1. In fact, I was just looking at some stuff about the Wilson preselector, which is an ingenious device.

      Part of the reason I’ve written so much about Hydra-Matic is that I was amazed at how the earlier versions have fallen into obscurity — which is amazing when you consider their production volume. Most mechanically inclined automotive people are probably still reasonably familiar with Turbo Hydra-Matic, TorqueFlite, and the C4/C6, but the older ones are now poorly understood (and some, notably the dual- and triple turbine torque converter transmissions, weren’t that well understood when new!).

  2. My daily driver (by choice) is an ’89 Wrangler. Probably one of the last applications of the classic Torqueflite. Three speeds, no lock up, no overdrive, no electronics. Not all that efficient, but over 300k with a single tear down for new seals.

  3. Another system that saw service with UK’s BMC and its later incarnations was the 4 speed AP (Automotive Products) automatic transmission.
    When it was working properly it was an excellent transmission, making automatic versions of the original Mini and Austin 1100 (sold as the Austin America in the USA), and the Austin Maxi. The Mini and 1100 models suffered very little performance penalty compared with stick cars, the Maxi had a 5 speed stick shift, so the automatic suffered in comparison.
    The designers managed to cram it underneath the engine as in the stick transmission. Even more remarkably, they persuaded it to work sharing the engine oil. However the latter may have proved not such a great idea, they had a very short lifespan, typically 30-40,000 miles. If it had its own separate lubrication I think that would have helped improve its durability.
    It has long been confined to history now, like so many British innovations lack of investment and development meant it fell by the wayside.

    1. I know of the AP automatic, and of the earlier AP Manumatic, but I confess I haven’t ever investigated its innards!

  4. Thank you for taking the time to explain all of this as well as you do. I’ve poked my head around inside a few automatic transmissions but never to this level of detail.

    Of note: You could still find this same layout in use in 2001. Chrysler was unable to prevent their Electronic Ultradrive 40TE from overheating in the Neon compact car. It was then fitted it with the 31TH(A413) TorqueFlite from 1995-2001. A version of the A904 TorqueFlite with a transfer gearset on the output shaft to connect the power back to a center mounted differential due to the cars transverse layout. The only electronics was a solenoid to engage the lockup clutch in the torque converter. Sadly even the high stall converter used couldn’t overcome the fact that you didn’t shift to 2nd gear until 55mph. Giving the car a reputation of being painfully slow.

    1. Yeah, the TorqueFlite survived a remarkably long time, although it really ended up dragging down the image of the Neon (especially in the U.K.).

  5. A small nitpick (hope you don’t mind): On page 3 you surmise that a transmission could have 88, 40 and 24 teeth on its gears. While this is mathematically feasible, engineering practice shows that such an arrangement would result in severe and uneven wear of the gears in question. The preferred arrangement is a hunting tooth arrangement – no common denominator for the gears in contact, ensuring even wear.

    (Imagine a gear whose last tooth was not given the final pass during machining, resulting in a slight profile shift of the tooth. If it were always in contact with 1 or 2 teeth on the opposite gear these would wear rapidly, resulting in an uneven transmission of force as they mesh and come out of contact, which in turn would increase the wear rate even more.)

    1. I hadn’t considered that point when I wrote that section, but you’re right. I should probably see again if I can find actual gear teeth counts, which would be the best solution.

    2. Okay, I was able to determine now that the transmission in question (early TorqueFlite) had actual gear teeth counts of 62, 21, and 28 teeth, giving ratios of 2.452/1.452/1.000 and -2.214, and I’ve amended the text accordingly.

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