Bombsight
A bombsight is a device used by military aircraft to drop bombs accurately. Bombsights, a feature of combat aircraft since World War I, were first found on purpose-designed bomber aircraft and then moved to fighter-bombers and modern tactical aircraft as those aircraft took up the brunt of the bombing role.
A bombsight has to estimate the path the bomb will take after release from the aircraft. The two primary forces during its fall are gravity and air drag, which make the path of the bomb through the air roughly parabolic. There are additional factors such as changes in air density and wind that may be considered, but they are concerns only for bombs that spend a significant portion of a minute falling through the air. Those effects can be minimized by reducing the fall time by low-level bombing or by increasing the speed of the bombs. Those effects are combined in the dive bomber.
However, low-level bombing also increases the danger to the bomber from ground-based defences, so accurate bombing from higher altitudes has always been desired. That has led to a series of increasingly sophisticated bombsight designs dedicated to high-altitude level bombing.
Bombsights were first used before World War I and have since gone through several major revisions. The earliest systems were iron sights, which were pre-set to an estimated fall angle. In some cases, they consisted of nothing more than a series of nails hammered into a convenient spar, lines drawn on the aircraft, or visual alignments of certain parts of the structure. They were replaced by the earliest custom-designed systems, normally iron sights that could be set based on the aircraft's airspeed and altitude. These early systems were replaced by the vector bombsights, which added the ability to measure and adjust for winds. Vector bombsights were useful for altitudes up to about and speeds up to about.
In the 1930s, mechanical computers with the performance needed to solve the equations of motion started to be incorporated into the new tachometric bombsights, the most famous of which is the Norden. Then, in World War II, tachometric bombsights were often combined with radar systems to allow accurate bombing through clouds or at night. When postwar studies demonstrated that bomb accuracy was roughly equal either optically or radar-guided, optical bombsights were generally removed and the role passed to dedicated radar bombsights. Finally, especially since the 1960s, fully computerized bombsights were introduced, which combined the bombing with long-range navigation and mapping.
Modern aircraft do not have a bombsight but use highly computerized systems that combine bombing, gunnery, missile fire and navigation into a single head-up display. The systems have the performance to calculate the bomb trajectory in real time, as the aircraft manoeuvres, and add the ability to adjust for weather, relative altitude, relative speeds for moving targets and climb or dive angle. That makes them useful both for level bombing, as in earlier generations, and tactical missions, which used to bomb by eye.
Theory
Forces on a bomb
The drag on a bomb for a given air density and angle of attack is proportional to the relative air speed squared. If the vertical component of the velocity is denoted by and the horizontal component by then the speed is and the vertical and horizontal components of the drag are:where is the coefficient of drag, is the cross-sectional area, and is the air density. These equations show that horizontal velocity increases vertical drag and vertical velocity increases horizontal drag. These effects are ignored in the following discussion.
To start with, consider only the vertical motion of a bomb. In this direction, the bomb will be subject to two primary forces, gravity and drag, the first constant, and the second varying with the square of velocity. For an aircraft flying straight and level, the initial vertical velocity of the bomb will be zero, which means it will also have zero vertical drag. Gravity will accelerate the bomb downwards, and as its velocity increases so does the drag force. At some point, the force of drag will become equal to the force of gravity, and the bomb will reach terminal velocity. As the air drag varies with air density, and thus altitude, the terminal velocity will decrease as the bomb falls. Generally, the bomb will slow as it reaches lower altitudes where the air is denser, but the relationship is complex.
Now consider the horizontal motion. At the instant it leaves the shackles, the bomb carries the forward speed of the aircraft with it. This momentum is countered solely by drag, which starts to slow the forward motion. As the forward motion slows, the drag force drops and this deceleration diminishes. The forward speed is never reduced entirely to zero. If the bomb were not subject to drag, its path would be purely ballistic and it would impact at an easily calculable point, the vacuum range. In practice, drag means that the impact point is short of the vacuum range, and this real-world distance between dropping and impact is known simply as the range. The difference between the vacuum range and actual range is known as the trail because the bomb appears to trail behind the aircraft as it falls. The trail and range differ for different bombs due to their individual aerodynamics and typically have to be measured on a bombing range.
The main problem in completely separating the motion into vertical and horizontal components is the terminal velocity. Bombs are designed to fly with the nose pointed forward into the relative wind, normally through the use of fins at the back of the bomb. The drag depends on the angle of attack of the bomb at any given instant. If the bomb is released at low altitudes and speeds the bomb will not reach terminal velocity and its speed will be defined largely by how long the bomb has been falling.
Finally, consider the effects of wind. The wind acts on the bomb through drag and is thus a function of the wind speed. This is typically only a fraction of the speed of the bomber or the terminal velocity, so it only becomes a factor if the bomb is dropped from altitudes high enough for this small influence to noticeably affect the bomb's path. The difference between the impact point and where it would have fallen if there had been no wind is known as drift, or cross trail.
The bombsight problem
In ballistics terms, it is traditional to talk of the calculation of aiming of ordnance as the solution. The bombsight problem is the calculation of the location in space where the bombs should be dropped in order to hit the target when all of the effects noted above are taken into account.In the absence of wind, the bombsight problem is fairly simple. The impact point is a function of three factors, the aircraft's altitude, its forward speed, and the terminal velocity of the bomb. In many early bombsights, the first two inputs were adjusted by separately setting the front and back sights of an iron sight, one for the altitude and the other for the speed. Terminal velocity, which extends the fall time, can be accounted for by raising the effective altitude by an amount that is based on the bomb's measured ballistics.
When windage is accounted for, the calculations become more complex. As the wind can operate in any direction, bombsights generally break the windage into the portions that act along the flight path and across it. In practice, it was generally simpler to have the aircraft fly in such a way to zero out any sideways motion before the drop, and thereby eliminate this factor. This is normally accomplished using a common flying techniques known as crabbing or sideslip.
Bombsights are sighting devices that are pointed in a particular direction, or aimed. Although the solution outlined above returns a point in space, simple trigonometry can be used to convert this point into an angle relative to the ground. The bombsight is then set to indicate that angle. The bombs are dropped when the target passes through the sights. The distance between the aircraft and target at that moment is the range, so this angle is often referred to as the range angle, although dropping angle, aiming angle, bombing angle and similar terms are often used as well. In practice, some or all of these calculations are carried out using angles and not points in space, skipping the final conversion.
Accuracy
The accuracy of the drop is affected both by inherent problems like the randomness of the atmosphere or bomb manufacture as well as more practical problems like how close to flat and level the aircraft is flying or the accuracy of its instruments. These inaccuracies compound over time, so increasing the altitude of the bomb run, thereby increasing the fall time, has a significant impact on the final accuracy of the drop.It is useful to consider a single example of a bomb being dropped on a typical mission. In this case we will consider the AN-M64 500 lbs General-Purpose Bomb, widely used by the USAAF and RAF during World War II, with direct counterparts in the armouries of most forces involved. Ballistic data on this bomb can be found in "Terminal Ballistic Data, Volume 1: Bombing". Against men standing in the open, the 500 lbs has a lethal radius of about, but much less than that against buildings, perhaps.
The M64 will be dropped from a Boeing B-17 flying at at an altitude of 20,000 feet in a wind. Given these conditions, the M64 would travel approximately forward from the drop point before impact, for a trail of about from the vacuum range, and impact with a velocity of 351 m/s at an angle of about 77 degrees from horizontal. A wind would be expected to move the bomb about during that time. The time to fall is about 37 seconds.
Assuming errors of 5% in every major measurement, one can estimate those effects on accuracy based on the methodology and tables in the guide. A 5% error in altitude at 20,000 feet would be 1,000 feet, so the aircraft might be anywhere from 19 to 21,000 feet. According to the table, this would result in an error around 10 to 15 feet. A 5% error in airspeed, 10 mph, would cause an error of about 15 to 20 feet. In terms of drop timing, errors on the order of one-tenth of a second might be considered the best possible. In this case, the error is simply the ground speed of the aircraft over this time, or about 30 feet. All of these are well within the lethal radius of the bomb.
The wind affects the accuracy of the bomb in two ways, pushing directly on the bomb while it falls, as well as changing the ground speed of the aircraft before the drop. In the case of the direct effects on the bomb, a measurement that has a 5% error, 1.25 mph, that would cause a 5% error in the drift, which would be 17.5 feet. However, that 1.25 mph error, or 1.8 fps, would also be added to the aircraft's velocity. Over the time of the fall, 37 seconds, that would result in an error of 68 feet, which is at the outside limit of the bomb's performance.
The measurement of the wind speed is a more serious concern. Early navigation systems generally measured it using a dead reckoning procedure that compares measured movement over the ground with the calculated movement using the aircraft instruments. The Federal Aviation Administration's FAR Part 63 suggests 5 to 10% accuracy of these calculations, the US Air Force's AFM 51-40 gives 10%, and the US Navy's H.O. 216 at a fixed 20 miles or greater. Compounding this inaccuracy is that it is made using the instrument's airspeed indication, and as the airspeed in this example is about 10 times that of the wind speed, its 5% error can lead to great inaccuracies in wind speed calculations. Eliminating this error through the direct measurement of ground speed was a major advance in the tachometric bombsights of the 1930s and 40s.
Finally, consider errors of the same 5% in the equipment itself, that is, an error of 5% in the setting of the range angle, or a similar 5% error in the levelling of the aircraft or bombsight. For simplicity, consider that 5% to be a 5 degree angle. Using simple trigonometry, 5 degrees at 20,000 feet is approximately 1,750 feet, an error that would place the bombs far outside their lethal radius. In tests, accuracies of 3 to 4 degrees were considered standard, and angles as high as 15 degrees were not uncommon. Given the seriousness of the problem, systems for automatic levelling of bombsights was a major area of study before World War II, especially in the US.