December 1958 Radio-Electronics
These articles are scanned and OCRed from old editions of the Radio & Television News magazine. Here is a list of
articles I have already posted. All copyrights are hereby acknowledged.
von Braun and his team of rocket scientists are credited with developing
the first useful inertial stabilization platforms for ballistic
missiles. The infamous and formidable
wreaked terror upon the heads of Londoners during the latter days
of World War II. It served to keep the rocket in a fixed orientation
during the boost phase of the flight, but did not serve any active
targeting function. Inertial navigation systems, on the other hand,
are used to provide both accurate positional and attitude information
for the pilot (if the platform has one) and to steer the platform
(vehicle) to a predetermined destination. Inertial nav systems are
therefore much more complex. Early inertial navigation systems relied
on physical spinning gyroscopes mounted within a series of nearly
frictionless gimbals to maintain a fixed reference position in space.
Contactless encoders about the rotation axes of the gimbals sent
positional information to a computer, which then performed necessary
calculations and sent formatted data to visual flight instruments
(if present) and to control surface actuators (elevator, aileron,
rudder, throttle, trim tabs, etc.) to direct the craft. As with
every other aspect of electronics and mechanics, we have come a
long way with inertial navigation systems since 1958 - most significantly
having replaced the rotating mechanical gyroscope with optical versions.
Accuracy, immunity to perturbances, stability, ease of manufacturing,
cost, and size have all been improved incredibly.
Inertial Guidance Directs Planes and Missiles
By Philip Julian
Electronic computers, gyroscopes and accelerometers, when properly
combined, form a sensitive guidance system that leads a guided vehicle
to any spot on earth.
Fig. 2 - The stable platform consists of two or three
gyroscopes, plus two or three accelerometers mounted in
a gimbal arrangement which allows gyros to keep the accelerometers
fixed in space, no matter how the vehicle moves. (Courtesy
of Aviation Week)
(top) Accelerometer used in 5,000·mile range ballistic
(bottom) Gyroscope used in 5,000-mile range missiles
has extremely low drift rate.
A new technique called "inertial guidance" enables man to match
the ability of birds to navigate unerringly over distances of thousands
of miles without using radio or radar. Furthermore, the inertial-guidance
system can operate in weather so bad that the birds are grounded.
Inertial guidance will direct our new intercontinental ballistic
missiles (ICBM's) to targets 5,000 miles away and will also direct
our newest bombers, the supersonic B-58 and hypersonic B-70, to
their targets. It recently was used to guide the submarine Nautilus
on its polar mission.
An inertial-guidance system is completely self-contained in the
missile or airplane. It does not require ground-based radio or radar
stations for assistance, nor does it radiate any electromagnetic
energy itself. Inertial systems do, however, make extensive use
There are a variety of possible inertial system configurations,
depending upon the intended mission. However, all operate on the
same basic principle - measuring accelerations of the missile or
airplane throughout the guided portion of its flight. From these
measured accelerations an airborne computer system can calculate
how far the vehicle has traveled and in what direction.
Fig. 1 - Cutaway view of a simple accelerometer. Any
acceleration of the vehicle in which the device is mounted
causes the mass to be displaced from the center, producing
a signal which is proportional to the acceleration.
The only data the inertial system computer needs is the position
of the target relative to the takeoff point. The computer then continuously
calculates the vehicle's position, compares it with the desired
course-to-target, and generates signals which automatically steer
the vehicle onto the correct course .
Because inertial systems are completely self-contained, do not
themselves radiate any electromagnetic energy and do not need ground-based
radio-radar stations, they offer several important military advantages:
Jam-proofness: There is no known way to jam or confuse an inertial
system. By contrast, guidance systems which use radio or radar can
be jammed or disrupted by enemy electronic countermeasures equipment.
Security: Unlike radio-radar guidance whose electromagnetic radiation
tips off enemy that the vehicle is coming, making it possible to
launch intercepting aircraft or missiles, inertial guidance gives
no advance warning to the enemy.
Mobility: Since inertially guided missiles require no large ground-based
guidance system installations, they can be launched from hidden
sites or quickly moved to other locations.
Certain limitations or disadvantages are, however, inherent in
inertial systems. For example, an inertial system is extremely costly
because of the extreme precision required to fabricate its components.
Also, errors build up with time, so accuracy is reduced on long
missions. However, there are ingenious ways for getting around this
How does it work?
To understand how an inertial system operates, we must first
examine the basic fundamentals. These are quite simple. If you were
told that an automobile had started from rest and was accelerating
uniformly at the rate of 10 feet per second every second, you could
calculate its distance at any given instant. The formula is:
Distance = 1/2 at2, where a is acceleration and t is
For example, after 1 second the car will have covered a total
distance of 5 feet (1/2 x 10 x 1). At end of 2 seconds the auto
will have moved a total of 20 feet, and after 3 seconds a total
of 45 feet.
If the car were equipped with a device which could measure and
indicate the acceleration, and if we had a stop watch, scratch pad
and pencil, we could always calculate how far we had traveled.
Naturally, in a car equipped with an odometer-speedometer, there
is no point in going to such trouble to determine how far we have
traveled. But in an airplane or missile there is no such easy way
of measuring distance covered and hence we turn to inertial guidance.
An inertial system continuously runs through the mathematical calculation
of the D = 1/2 at2 equation.
The stable platform on the right is undergoing a final
series of tests to check its accuracy.
To perform this computation, the inertial system must continuously
measure vehicle acceleration relative to the earth. To do this,
the system employs devices known as "accelerometers." One of them
is installed in the aircraft or missile to measure accelerations
along its fore-aft axis. Another is installed so as to measure accelerations
at right angles to the fore-aft axis - corresponding to a line drawn
through the vehicle's wings (or where its wings would be if it had
them). In certain applications, primarily ballistic missiles, a
third accelerometer is installed to sense accelerations at right
angles to the other two, essentially up-down accelerations relative
to the earth.
In principle, these accelerometers are very simple devices, but
in practice they become very complex to achieve the extremely high
sensitivity and accuracy required. The simplest type of accelerometer
consists of a weight (mass) which is suspended in an enclosure by
two springs (see Fig. 1).
When the accelerometer is at rest (zero acceleration), the mass
is centered relative to its enclosure by the supporting springs.
If the enclosure is suddenly moved along its sensitive axis (line
running through springs and weight), the weight will try to "sit
tight," until it is forced to come along with the enclosure by the
forces exerted by the springs. This follows Newton's laws of motion
which say that a body at rest tends to remain at rest unless acted
upon by outside forces.
The amount that the weight is displaced from its center (zero-acceleration)
position inside its enclosure is in direct proportion to the magnitude
of the acceleration applied to the enclosure. If a small electrical
pickoff (potentiometer, synchro, etc.) is added to measure displacement
of the weight from its center position, the signal generated by
the pickoff will be proportional to acceleration, and the complete
device will function as an accelerometer.
Because the accuracy of the inertial guidance system can be no
better than the accuracy of its accelerometers, more elaborate and
more complex accelerometers than the one described must be used.
The problem is made more difficult because of the wide range of
accelerations the device must measure - from perhaps 100 G (100
times the acceleration of gravity) to a few thousandths or millionths
of a G.
Some inertial systems employ what are called "integrating accelerometers,"
which sense acceleration and simultaneously perform the operation
of "integration" so that their output signal is directly proportional
to the vehicle's velocity or distance traveled. The integrating
accelerometer is more complex than the elementary accelerometer,
but simplifies the calculations which must be performed by the system's
In one respect, Nature appears to have conspired to make inertial
guidance systems impractical. This problem arises because the accelerometer
which reacts to the vehicle accelerations it seeks to measure also
responds to the force of gravity which it should ignore.
Thus an accelerometer intended to measure horizontal accelerations
along the fore-aft axis of an airplane or missile would correctly
sense no acceleration when the vehicle is at rest, so long as the
accelerometer is truly horizontal. But if the vehicle and accelerometer
were slightly off level, the accelerometer weight would be deflected
from center by gravity, and the inertial guidance system would "think"
the vehicle had taken off when in fact it was still at rest.
If this were the extent of the problem, it could be easily solved
by leveling up the accelerometers before turning on the inertial
system prior to takeoff. But even if this were done, the missile
or airplane obviously is not going to maintain a perfectly level
attitude once it has been launched.
The basic problem, then, is how to keep the accelerometers in
position throughout the mission to prevent them from sensing gravity
and confusing it with acceleration due to actual vehicle motion.
For a solution, inertial system designer - turn to the gyroscope,
a device that tries to hold its angular position always fixed in
space. The simple spinning top, or the toy gyro which children find
so amusing, demonstrates this principle.
The stable platform
A basic gyro consists of a small flywheel spun at extremely high
speeds, usually by an electric motor. The shaft about which the
flywheel rotates is called the "spin axis," and it is this which
the gyro seeks to hold fixed in space.
Inertial guidance gyros, accelerometers and other critical
components are assembled, inspected and tested in air-conditioned
dust-free rooms to prevent contamination and resultant inaccuracies.
If the gyro's spin axis is supported in a suitable frame, called
a "gimbal," and this frame is in turn supported inside a larger
gimbal, so that the outer frame can be rotated freely about the
inner spin-axis gimbal, we have a simple gyro. In practice, many
gyros have still a third gimbal which supports the other two.
When the gyro's flywheel has been brought up to speed, the outer
gimbal (s) can be rotated or moved to any position without disturbing
the position of the spin axis - just as if it were locked onto a
If such a gyro is installed in an airplane or missile, with its
supporting gimbal (s) attached to the vehicle's structure, the gyro
will try to keep its spin axis fixed in space regardless of changes
in vehicle attitude during the flight.
If the spin axis is aligned with the true vertical before takeoff,
the gyro will seek to hold this same position throughout the mission.
And if the accelerometers are, in effect, mounted on the gyro spin
axis (at right angles to it), they will remain horizontal throughout
the flight and cannot sense the unwanted gravity acceleration.
If another gyro is installed so that its spin axis is horizontal,
instead of vertical, and aligned with true north, this gyro will
try to keep itself aligned with north during the flight. This provides
a heading reference by which the inertial system can resolve vehicle
movement into distance traveled in north-south and east-west directions.
Inertial systems usually employ two or three gyros, depending
upon the type of gyro used. There are certain advantages and disadvantages
to each type of configuration.
The combination of gyros, accelerometers, their supporting gimbals
and related mechanisms is called a "gyro-stabilized platform," or
sometimes "stabilized platform," for short (see Fig. 2).
If gyros kept their spin axes fixed in space indefinitely, the
problem of designing an inertial system would be easy, but once
again Nature conspires to make the problem difficult. In practice,
a shift in the position of the spinning gyro flywheel on its shaft
of a few millionths of an inch can make the gyro wander ("drift")
from its original position. A speck of dirt or a metal chip too
small to be seen by the human eye, except through a microscope,
in one of the gyro gimbal bearings can also introduce serious errors
in gyro performance.
Any such drift in the position of the gyro spin axis tilts the
accelerometers off horizontal, causing them to sense gravity acceleration,
or shifts the heading reference, making the system think the vehicle
is moving in a different direction than it actually is.
At the end of World War II, the gyros used in aircraft flight
instruments (to indicate airplane attitude and heading) had drift
rates of about 15° per hour. If inertial systems used such gyros,
guidance accuracy would be completely unacceptable.
Today, industry builds gyros which have drift rates of only .01°
per hour. Such a gyro has less drift after 2 months of operation
than the post-war flight gyros experienced in a single hour. Gyros
with still lower drift rates are under development.
To build such extremely accurate gyros, manufacturers must assemble
them in ultra-clean air-conditioned rooms where the air is continuously
filtered to keep out microscopic-size particles of dust. Employees
must wear lint-free nylon hats and coveralls, and coats and tools
are cleaned at least once a day. No one can enter without passing
through airlocks equipped with high-power blowers which dust him
Individual parts that go into the gyro are inspected under microscopes
for possible burrs which might work loose and find their way into
bearings. Deburring is done under a microscope, using precision
The thinking heart
The heart of any inertial system is the computer which integrates
acceleration signals to determine distance traveled, resolves this
into distance covered in north-south and east-west directions, then
compares this with the path the vehicle must fly to hit its target,
and finally it calculates what signals must be sent to vehicle's
controls to maneuver it onto the desired course.
These computations must be performed from takeoff throughout
the guided portion of the mission. For a ballistic missile, where
guidance lasts only several minutes (from there on the missile behaves
like an unguided projectile), the computer must work at lightning
speed and with extreme accuracy. Unless errors in missile path are
quickly corrected, the missile may go out of control or miss the
intended target by a wide margin.
Most of the new inertial systems under development use tiny digital
computers. These are first cousins to the familiar giant computing
brains, but have been so miniaturized that they occupy no more than
a couple of cubic feet in volume. Some of the newer airborne digital
computers for inertial system use occupy less than 1 cubic foot.
To reduce computer size, designers have gone to all-transistor
models. One such computer, being developed for intercontinental
ballistic missiles, uses approximately 1,200 transistors and 10,000
diodes. Choice of targets is made by plugging appropriate subassemblies
into the computer.
Although industry's designers have made remarkable progress in
the past 10 years in improving the performance of gyros and accelerometers,
an extremely stiff price must be paid in terms of manufacturing
and inspection cost to hold down errors in inertial systems intended
for use on long missions.
For example, an inertial navigation-bombing system for use in
a 1,000-mph bomber, like the B-58, must maintain good accuracy for
5 hours to reach a target 5,000 miles away. This is more than 60
times the period that an inertial system must provide guidance for
an ICBM. This means that gyro drift errors accumulate for 60 times
as long and hence can be something like 60 times greater.
Fortunately, Nature lends a helping hand here in the form of
a principle first suggested in 1923 by Dr. Maxmillian Schuler, a
German professor of applied mechanics. Applying this principle of
the "84-minute pendulum," to provide what often is called a "Schuler-tuned"
inertial system, greatly reduces error buildup on long missions
by effectively washing out gyro drift and some, but not all, of
the accumulated errors approximately every 84 minutes.
Even with Schuler tuning, it is not easy to get the high-precision
accuracies required for long military missions. Another approach
which eases the accuracies required of gyros and accelerometers
is to combine the inertial system with some other navigation technique
to form a hybrid system.
One such hybrid system uses a small airborne Doppler radar which
measures the vehicle's ground speed accurately. The Doppler radar
is used to correct for errors in acceleration measurement while
the vehicle is over friendly territory where its electromagnetic
radiation does not give it away. Once the vehicle approaches enemy
territory, Doppler radar can be turned off and the system operated
as a pure inertial system.
Another possible hybrid system configuration combines inertial
and celestial navigation techniques. Electro-optical devices are
available which automatically track a star, determining its azimuth
(direction) and elevation position. Two such devices, together with
a vertical reference such as a stabilized platform provides, furnish
enough information for a computer to calculate the vehicle's position.
Such periodic star fixes can be used to correct any accumulation
of errors in the inertial system when suitable stars are available
for sighting. When clouds prevent obtaining a star sight, the system
reverts to its pure inertial mode of operation.
Size, weight and cost of an inertial guidance system depend upon
its intended use, including such factors as mission duration and
required accuracy. Although exact figures are not available because
of military security considerations, an inertial guidance system
for ballistic missiles is believed to weigh between 400 and 500
pounds, including the computer. A single system probably costs in
the neighborhood of $250,000.
With developments now under way, weight of such an inertial system
ought to come down to perhaps 200 pounds and its price down to perhaps
$150,000. For short-range uses, such as in helicopters for navigation
where mission times are measured in minutes and extreme accuracy
is not required, it is possible to build an inertial guidance system
today which weighs less than 100 pounds.
Despite its weight and price, which are high compared to other
navigation guidance techniques, the many attractive military advantages
of inertial guidance suggest it will find increasing use in new
military missiles and aircraft.
Posted August 14, 2014