The Bendix Central Air Data Computer (CADC) is an electromechanical analog computer that uses gears and cams for its mathematics. It was a key part of military planes such as the F-101 and the F-111 fighters, computing airspeed, Mach number, and other "air data". The rotating gears are powered by six small servomotors, so these motors are in a sense the fundamental component of the CADC. In the photo below, you can see one of the cylindrical motors near the center, about 1/3 of the way down.

The servomotors in the CADC are unlike standard motors. Their name—"Motor-Tachometer Generator" or "Motor and Rate Generator"1—indicates that each unit contains both a motor and a speed sensor. Because the motor and generator use two-phase signals, there are a total of eight colorful wires coming out, many more than a typical motor. Moreover, the direction of the motor can be controlled, unlike typical AC motors. I couldn't find a satisfactory explanation of how these units worked, so I bought one and disassembled it. This article (part 5 of my series on the CADC2) provides a complete teardown of the motor/generator and explain how it works.

The image below shows a closeup of two motors powering one of the pressure signal outputs. Note the bundles of colorful wires to each motor, entering in two locations. At the top, the motors drive complex gear trains. The high-speed motors are geared down by the gear trains to provide much slower rotations with sufficient torque to power the rest of the CADC's mechanisms.

The motor/tachometer that we disassembled is shorter than the ones in the CADC (despite having the same part number), but the principles are the same. We started by removing a small C-clip on the end of the motor and and unscrewing the end plate. The unit is pretty simple mechanically. It has bearings at each end for the rotor shaft. There are four wires for the motor and four wires for the tachometer.3

The rotor (below) has two parts on the shaft. the left part is for the motor and the right drum is for the tachometer. The left part is a squirrel-cage rotor4 for the motor. It consists of conducting bars (light-colored) on an iron core. The conductors are all connected at both ends by the conductive rings at either end. The metal drum on the right is used by the tachometer. Note that there are no electrical connections between the rotor components and the rest of the motor: there are no brushes or slip rings. The interaction between the rotor and the windings in the body of the motor is purely magnetic, as will be explained.

The motor/tachometer contains two cylindrical stators that create the magnetic fields, one for the motor and one for the tachometer. The photo below shows the motor stator inside the unit after removing the tachometer stator. The stators are encased in hard green plastic and tightly pressed inside the unit. In the center, eight metal poles are visible. They direct the magnetic field onto the rotor.

The photo below shows the stator for the tachometer, similar to the stator for the motor. Note the shallow notches that look like black lines in the body on the lower left. These are probably adjustments to the tachometer during manufacturing to compensate for imperfections. The adjustments ensure that the magnetic fields are nulled out so the tachometer returns zero voltage when stationary. The metal plate on top shields the tachometer from the motor's magnetic fields.

The poles and the metal case of the stator look solid, but they are not. Instead, they are formed from a stack of thin laminations. The reason to use laminations instead of solid metal is to reduce eddy currents in the metal. Each lamination is varnished, so it is insulated from its neighbors, preventing the flow of eddy currents.

In the photo below, I removed some of the plastic to show the wire windings underneath. The wires look like bare copper, but they have a very thin layer of varnish to insulate them. There are two sets of windings (orange and blue, or red and black) around alternating metal poles. Note that the wires run along the pole, parallel to the rotor, and then wrap around the pole at the top and bottom, forming oblong coils around each pole.5 This generates a magnetic field through each pole.

The motor

The motor part of the unit is a two-phase induction motor with a squirrel-cage rotor.6 There are no brushes or electrical connections to the rotor, and there are no magnets, so it isn't obvious what makes the rotor rotate. The trick is the "squirrel-cage" rotor, shown below. It consists of metal bars that are connected at the top and bottom by rings. Assume (for now) that the fixed part of the motor, the stator, creates a rotating magnetic field. The important principle is that a changing magnetic field will produce a current in a wire loop.7 As a result, each loop in the squirrel-cage rotor will have an induced current: current will flow up9 the bars facing the north magnetic field and down the south-facing bars, with the rings on the end closing the circuits.

But how does the stator produce a rotating magnetic field? And how do you control the direction of rotation? The next important principle is that current flowing through a wire produces a magnetic field.8 As a result, the currents in the squirrel cage rotor produce a magnetic field perpendicular to the cage. This magnetic field causes the rotor to turn in the same direction as the stator's magnetic field, driving the motor. Because the rotor is powered by the induced currents, the motor is called an induction motor.

The diagram below shows how the motor is wired, with a control winding and a reference winding. Both windings are powered with AC, but the control voltage either lags the reference winding by 90° or leads the reference winding by 90°, due to the capacitor. Suppose the current through the control winding lags by 90°. First, the reference voltage's sine wave will have a peak, producing the magnetic field's north pole at A. Next (90° later), the control voltage will peak, producing the north pole at B. The reference voltage will go negative, producing a south pole at A and thus a north pole at C. The control voltage will go negative, producing a south pole at B and a north pole at D. This cycle will repeat, with the magnetic field rotating counter-clockwise from A to D. Conversely, if the control voltage leads the reference voltage, the magnetic field will rotate clockwise. This causes the motor to spin in one direction or the other, with the direction controlled by the control voltage. (The motor has four poles for each winding, rather than the one shown below; this increases the torque and reduces the speed.)

The purpose of the capacitor is to provide the 90° phase shift so the reference voltage and the control voltage can be driven from the same single-phase AC supply (in this case, 26 volts, 400 hertz). Switching the polarity of the control voltage reverses the direction of the motor.

There are a few interesting things about induction motors. You might expect that the motor would spin at the same rate as the rotating magnetic field. However, this is not the case. Remember that a changing magnetic field induces the current in the squirrel-cage rotor. If the rotor is spinning at the same rate as the magnetic field, the rotor will encounter an unchanging magnetic field and there will be no current in the bars of the rotor. As a result, the rotor will not generate a magnetic field and there will be no torque to rotate it. The consequence is that the rotor must spin somewhat slower than the magnetic field. This is called "slippage" and is typically a few percent of the full speed, with more slippage as more torque is required.

Many household appliances use induction motors, but how do they generate a rotating magnetic field from a single-phase AC winding? The problem is that the magnetic field in a single AC winding will just flip back and forth, so the motor will not turn in either direction. One solution is a shaded-pole motor, which puts a copper bar around part of each pole to break the symmetry and produce a weakly rotating magnetic field. More powerful induction motors use a startup winding with a capacitor (analogous to the control winding). This winding can either be switched out of the circuit once the motor starts spinning,10 or used continuously, called a permanent-split capacitor (PSC) motor. The best solution is three-phase power (if available); a three-phase winding automatically produces a rotating magnetic field.

Tachometer/generator

The second part of the unit is the tachometer generator, sometimes called the rate unit.11 The purpose of the generator is to produce a voltage proportional to the speed of the shaft. The unusual thing about this generator is that it produces a 400-hertz output that is either in phase with the input or 180° out of phase. This is important because the phase indicates which direction the shaft is turning. Note that a "normal" generator is different: the output frequency is proportional to the speed.

The diagram below shows the principle behind the generator. It has two stator windings: the reference coil that is powered at 400 Hz, and the output coil that produces the output signal. When the rotor is stationary (A), the magnetic flux is perpendicular to the output coil, so no output voltage is produced. But when the rotor turns (B), eddy currents in the rotor distort the magnetic field. It now couples with the output coil, producing a voltage. As the rotor turns faster, the magnetic field is distorted more, increasing the coupling and thus the output voltage. If the rotor turns in the opposite direction (C), the magnetic field couples with the output coil in the opposite direction, inverting the output phase. (This diagram is more conceptual than realistic, with the coils and flux 90° from their real orientation, so don't take it too seriously. As shown earlier, the coils are perpendicular to the rotor so the real flux lines are completely different.)

But why does the rotating drum change the magnetic field? It's easier to understand by considering a tachometer that uses a squirrel-cage rotor instead of a drum. When the rotor rotates, currents will be induced in the squirrel cage, as described earlier with the motor. These currents, in turn, generate a perpendicular magnetic field, as before. This magnetic field, perpendicular to the orginal field, will be aligned with the output coil and will be picked up. The strength of the induced field (and thus the output voltage) is proportional to the speed, while the direction of the field depends on the direction of rotation. Because the primary coil is excited at 400 hertz, the currents in the squirrel cage and the resulting magnetic field also oscillate at 400 hertz. Thus, the output is at 400 hertz, regardless of the input speed.

Using a drum instead of a squirrel cage provides higher accuracy because there are no fluctuations due to the discrete bars. The operation is essentially the same, except that the currents pass through the metal of the drum continuously instead of through individual bars. The result is eddy currents in the drum, producing the second magnetic field. The diagram below shows the eddy currents (red lines) from a metal plate moving through a magnetic field (green), producing a second magnetic field (blue arrows). For the rotating drum, the situation is similar except the metal surface is curved, so both field arrows will have a component pointing to the left. This creates the directed magnetic field that produces the output.

The servo loop

The motor/generator is called a servomotor because it is used in a servo loop, a control system that uses feedback to obtain precise positioning. In particular, the CADC uses the rotational position of shafts to represent various values. The servo loops convert the CADC's inputs (static pressure, dynamic pressure, temperature, and pressure correction) into shaft positions. The rotations of these shafts power the gears, cams, and differentials that perform the computations.

The diagram below shows a typical servo loop in the CADC. The goal is to rotate the output shaft to a position that exactly matches the input voltage. To accomplish this, the output position is converted into a feedback voltage by a potentiometer that rotates as the output shaft rotates.12 The error amplifier compares the input voltage to the feedback voltage and generates an error signal, rotating the servomotor in the appropriate direction. Once the output shaft is in the proper position, the error signal drops to zero and the motor stops. To improve the dynamic response of the servo loop, the tachometer signal is used as a negative feedback voltage. This ensures that the motor slows as the system gets closer to the right position, so the motor doesn't overshoot the position and oscillate. (This is sort of like a PID controller.)

The error amplifier and motor drive circuit for a pressure transducer are shown below. Because of the state of electronics at the time, it took three circuit boards to implement a single servo loop. The amplifier was implemented with germanium transistors (since silicon transistors were later). The transistors weren't powerful enough to drive the motors directly. Instead, magnetic amplifiers (the yellow transformer-like modules at the front) powered the servomotors. The large rectangular capacitors on the right provided the phase shift required for the control voltage.

Conclusions

The Bendix CADC used a variety of electromechanical devices including synchros, control transformers, servo motors, and tachometer generators. These were expensive military-grade components driven by complex electronics. Nowadays, you can get a PWM servo motor for a few dollars with the gearing, feedback, and control circuitry inside the motor housing. These motors are widely used for hobbyist robotics, drones, and other applications. It's amazing that servo motors have gone from specialized avionics hardware to an easy-to-use, inexpensive commodity.

Follow me on Twitter @kenshirriff or RSS for updates. I'm also on Mastodon as @oldbytes.space@kenshirriff. Thanks to Joe for providing the CADC. Thanks to Marc Verdiell for disassembling the motor.

Notes and references

The Bendix Central Air Data Computer (CADC) is an electromechanical analog computer that uses gears and cams for its mathematics. It was a key part of military planes such as the F-101 and the F-111 fighters, computing airspeed, Mach number, and other "air data". This article reverse-engineers the two pressure transducers, on the right in the photo below. It is part 3 of my series on the CADC.1

Aircraft have determined airspeed from air pressure for over a century. A port in the side of the plane provides the static air pressure,2 the air pressure outside the aircraft. A pitot tube points forward and receives the "total" air pressure, a higher pressure due to the speed of the airplane forcing air into the tube. The airspeed can be determined from the ratio of these two pressures, while the altitude can be determined from the static pressure.

But as you approach the speed of sound, the fluid dynamics of air change and the calculations become very complicated. With the development of supersonic fighter planes in the 1950s, simple mechanical instruments were no longer sufficient. Instead, an analog computer calculated the "air data" (airspeed, air density, Mach number, and so forth) from the pressure measurements. This computer then transmitted the air data electrically to the systems that needed it: instruments, weapons targeting, engine control, and so forth. Since the computer was centralized, such a system was called a Central Air Data Computer or CADC, manufactured by Bendix and other companies.

Each value in the Bendix CADC is indicated by the rotational position of a shaft. Compact electric motors rotated the shafts, controlled by magnetic amplifier servo loops. Gears, cams, and differentials performed computations, with the results indicated by more rotations. Devices called synchros converted the rotations to electrical outputs that controlled other aircraft systems. The CADC is said to contain 46 synchros, 511 gears, 820 ball bearings, and a total of 2,781 major parts (but I haven't counted). These components are crammed into a compact cylinder: 15 inches long and weighing 28.7 pounds.

The equations computed by the CADC are impressively complicated. For instance, one equation computes the Mach number $M$ from the total pressure \( P_t \) and the static pressure \( P_s \):3

\[~~~\frac{P_t}{P_s} = \frac{166.9215M^7}{( 7M^2-1)^{2.5}}\]

It seems incredible that these functions could be computed mechanically, but three techniques make this possible. The fundamental mechanism is the differential gear, which adds or subtracts values. Second, logarithms are used extensively, so multiplications and divisions become additions and subtractions performed by a differential, while square roots are calculated by gearing down by a factor of 2. Finally, specially-shaped cams implement functions: logarithm, exponential, and other one-variable functions.4 By combining these mechanisms, complicated functions can be computed mechanically.

The pressure transducers

In this article, I'm focusing on the pressure transducers and how they turn pressures into shaft rotations. The CADC receives two pressure inputs: the total pressure \( P_t \) from the pitot tube, and the static pressure \( P_s \) from the static pressure port.5 The CADC has two independent pressure transducer subsystems, one for total pressure and one for static pressure. The two pressure transducers make up the right half of the CADC. The copper pressure tube for the static pressure is visible on top of the CADC below. This tube feeds into the black-domed pressure sensor at the right. The gears, motors, and other mechanisms to the left of the pressure sensor domes generate shaft rotations that are fed into the remainder of the CADC for calculations.

The pressure transducer has a tricky job: it must measure tiny pressure changes, but it must also provide a rotational signal that has enough torque to rotate all the gears in the CADC. To accomplish this, the pressure transducer uses a servo loop that amplifies small pressure changes into accurate rotations. The diagram below provides an overview of the process. The pressure input causes a small movement in the bellows diaphragm. This produces a small shaft rotation that is detected by a sensitive inductive pickup. This signal is amplified and drives a motor with enough power to drive the output shaft. The motor is also geared to counteract the movement of the bellows. The result is a feedback loop so the motor's rotation tracks the air pressure, but provides much more torque. An adjustable cam corrects for any error produced by irregularities in the diaphragm response. This complete mechanism is implemented twice, once for each pressure input.

To summarize, as the pressure moves the diaphragm, the induction pick-up produces an error signal. The motor is driven in the appropriate direction until the error signal becomes zero. At this point, the output shaft rotation exactly matches the input pressure. The advantage of the servo loop is that the diaphragm only needs to move the sensitive inductive pickup, rather than driving the gears of the CADC, so the pressure reading is more accurate.

In more detail, the process starts with connections from the aircraft's pitot tube and static pressure port to the CADC. The front of the CADC (below) has connections for the total pressure and the static pressure. The CADC also has five round military connectors for electrical connections between the CADC and the rest of the aircraft. (The outputs from the CADC are electrical, with synchros converting the shaft rotations into electrical representations.) Finally, a tiny time clock at the upper right keeps track of how many hours the CADC has been in operation, so it can be maintained according to schedule.

The photo below shows the main components of the pressure transducer system. At the upper left, the pressure line from the CADC's front panel goes to the pressure sensor, airtight under a black dome. The error signal from the sensor goes to the amplifier, which consists of three boards. The amplifier's power transformer and magnetic amplifiers are the most visible components. The amplifier drives the motors to the left. There are two motors controlled by the amplifier: one for coarse adjustments and one for fine adjustments. By using two motors, the CADC can respond rapidly to large pressure changes, while also accurately tracking small pressure changes. Finally, the output from the motor goes through the adjustable cam in the middle before providing the feedback signal to the pressure sensor. The output from the transducer to the rest of the CADC is a shaft on the left, but it is in the middle of the CADC and isn't visible in the photo.

The pressure sensor

Each pressure sensor is packaged in a black airtight dome and is fed from its associated pressure line. Inside the sensor, two sealed metal bellows (below) expand or contract as the pressure changes. The bellows are connected to opposite sides of a metal shaft, which rotates as the bellows expand or contract. This shaft rotates an inductive pickup, providing the error signal. The servo loop rotates a second shaft that counteracts the rotation of the first shaft; this shaft and gears are also visible below.

The end view of the sensor below shows the inductive pickup at the bottom, with colorful wires for the input (400 Hz AC) and the output error signal. The coil visible on the inductive pickup is an anti-backlash spring to ensure that the pickup doesn't wobble back and forth. The electrical pickup coil is inside the inductive pickup and isn't visible.

The amplifier

Each transducer feedback signal is amplified by three circuit boards centered around magnetic amplifiers, transformer-like amplifiers that were popular before high-power transistors came along. The photo below shows how the amplifier boards are packed next to the transducers. The boards are complex, filled with resistors, capacitors, germanium transistors, diodes, relays, and other components.

I reverse-engineered the boards and created the schematic below. I'll discuss the schematic at a high level; click it for a larger version if you want to see the full circuitry. The process starts with the inductive sensor (yellow), which provides the error input signal to the amplifier. The first stage of the amplifier (blue) is a two-transistor amplifier and filter. From there, the signal goes to two separate output amplifiers to drive the two motors: fine (purple) and coarse (cyan).

The inductive sensor provides its error signal as a 400 Hz sine wave, with a larger signal indicating more error. The phase of the signal is 0° or 180°, depending on the direction of the error. In other words, the error signal is proportional to the driving AC signal in one direction and flipped when the error is in the other direction. This is important since it indicates which direction the motors should turn. When the error is eliminated, the signal is zero.

Each output amplifier consists of a transistor circuit driving two magnetic amplifiers. Magnetic amplifiers are an old technology that can amplify AC signals, allowing the relatively weak transistor output to control a larger AC output. The basic idea of a magnetic amplifier is a controllable inductor. Normally, the inductor blocks alternating current. But applying a relatively small DC signal to a control winding causes the inductor to saturate, permitting the flow of AC. Since the magnetic amplifier uses a small signal to control a much larger signal, it provides amplification.

In the early 1900s, magnetic amplifiers were used in applications such as dimming lights. Germany improved the technology in World War II, using magnetic amplifiers in ships, rockets, and trains. The magnetic amplifier had a resurgence in the 1950s; the Univac Solid State computer used magnetic amplifiers (rather than vacuum tubes or transistors) as its logic elements. However, improvements in transistors made the magnetic amplifier obsolete except for specialized applications. (See my IEEE Spectrum article on magnetic amplifiers for more history of magnetic amplifiers.)

In the CADC, magnetic amplifiers control the AC power to the motors. Two magnetic amplifiers are visible on top of the amplifier board stack, while two more are on the underside; they are the yellow devices that look like transformers. (Behind the magnetic amplifiers, the power transformer is labeled "A".)

The transistor circuit generates the control signal to the magnetic amplifiers, and the output of the magnetic amplifiers is the AC signal to the motors. Specifically, the CADC uses two magnetic amplifiers for each motor. One magnetic amplifier powers the motor to spin clockwise, while the other makes the motor spin counterclockwise. The transistor circuit will pull one magnetic amplifier winding low; the phase of the input signal controls which magnetic amplifier, and thus the motor direction. (If the error input signal is zero, neither winding is pulled low, both magnetic amplifiers block AC, and the motor doesn't turn.)6 The result of this is that the motor will spin in the correct direction based on the error input signal, rotating the mechanism until the mechanical output position matches the input pressure. The motors are "Motor / Tachometer Generator" units that also generate a voltage based on their speed. This speed signal is fed into the transistor amplifier to provide negative feedback, limiting the motor speed as the error becomes smaller and ensuring that the feedback loop doesn't overshoot.

The other servo loops in the CADC (temperature and position error correction) have one motor driver constructed from transistors and two magnetic amplifiers. However, each pressure transducer has two motor drivers (and thus four magnetic amplifiers), one for fine adjustment and one for coarse adjustment. This allows the servo loop to track the input pressure very closely, while also adjusting rapidly to larger changes in pressure. The coarse amplifier uses back-to-back diodes to block small changes; only input voltages larger than a diode drop will pass through and energize the coarse amplifier.

The CADC is powered by standard avionics power of 115 volts AC, 400 hertz. Each pressure transducer amplifier has a simple power supply running off this AC, using a multi-winding power transformer. A center-tapped winding and full wave rectifier produces DC for the transistor amplifiers. Other windings supply AC (controlled by the magnetic amplifiers) to power the motors, AC for the magnetic amplifier control signals, and AC for the sensor. The transformer ensures that the transducer circuitry is electrically isolated from other parts of the CADC and the aircraft. The power supply is indicated in red in the schematic above.

The schematic also shows test circuitry (blue). One of the features of the CADC is that it can be set to two test configurations before flight to ensure that the system is operating properly and is correctly calibrated.7 Two relays allow the pressure transducer to switch to one of two test inputs. This allows the CADC to be checked for proper operation and calibration. The test inputs are provided from an external board and a helical feedback potentiometer (Helipot) that provides simulated sensor input.

Getting the amplifiers to work was a challenge. Many of the capacitors in the CADC had deteriorated and failed, as shown below. Marc went through the CADC boards and replaced the bad capacitors. However, one of the pressure transducer boards still failed to work. After much debugging, we discovered that one of the new capacitors had also failed. Finally, after replacing that capacitor a second time, the CADC was operational.

The mechanical feedback loop

The amplifier boards energize two motors that rotate the output shaft,8 the coarse and fine motors. The outputs from the coarse and fine motors are combined through a differential gear assembly that sums its two input rotations.9 While the differential functions like the differential in a car, it is constructed differently, with a spur-gear design. This compact arrangement of gears is about 1 cm thick and 3 cm in diameter. The differential is mounted on a shaft along with three co-axial gears: two gears provide the inputs to the differential and the third provides the output. In the photo, the gears above and below the differential are the input gears. The entire differential body rotates with the sum, connected to the output gear at the top through a concentric shaft. The two thick gears inside the differential body are part of its mechanism.

(Differential gear assemblies are also used as the mathematical component of the CADC, as it performs addition or subtraction. Since most values in the CADC are expressed logarithmically, the differential computes multiplication and division when it adds or subtracts its inputs.)

The CADC uses cams to correct for nonlinearities in the pressure sensors. The cam consists of a warped metal plate. As the gear rotates, a spring-loaded vertical follower moves according to the shape of the plate. The differential gear assembly under the plate adds this value to the original input to obtain a corrected value. (This differential implementation is different from the one described above.) The output from the cam is fed into the pressure sensor, closing the feedback loop.

At the top, 20 screws can be rotated to adjust the shape of the cam plate and thus the correction factor. These cams allow the CADC to be fine-tuned to maximize accuracy. According to the spec, the required accuracy for pressure was "40 feet or 0.15 percent of attained altitude, whichever is greater."

Conclusions

The Bendix CADC was built at an interesting point in time, when computations could be done digitally or analog, mechanically or electrically. Because the inputs were analog and the desired outputs were analog, the decision was made to use an analog computer for the CADC. Moreover, transistors were available but their performance was limited. Thus, the servo amplifiers are built from a combination of transistors and magnetic amplifiers.

Modern air data computers are digital but they are still larger than you might expect because they need to handle physical pressure inputs. While a drone can use a tiny 5mm MEMS pressure sensor, air data computers for aircraft have higher requirements and typically use larger vibrating cylinder pressure sensors. Even so, at 45 mm long, the modern pressure sensor is dramatically smaller than the CADC's pressure transducer with its metal-domed bellows sensor, three-board amplifier, motors, cam, and gear train. Although the mechanical Bendix CADC seems primitive, this CADC was used by the Air Force until the 1980s. I guess if the system worked, there was no reason to update it.

I plan to continue reverse-engineering the Bendix CADC,10 so follow me on Twitter @kenshirriff or RSS for updates. I'm also on Mastodon as @oldbytes.space@kenshirriff. Thanks to Joe for providing the CADC. Thanks to Nancy Chen for obtaining a hard-to-find document for me. Marc Verdiell and Eric Schlaepfer are working on the CADC with me.

Notes and references