Saturn V rocket plume
 S-IC burn
The Saturn V was notorious for complex exhaust plumes.
The F1 first stage engines burn kerosene with liquid oxygen. As with all oil-based fuels, the exhaust is sooty. Because the mixture is fuel-rich, there is unburned kerosene which can ignite when it meets the oxygen of the atmosphere.
Notice the F1 backflow in the image. It appears that the flame has climbed up the sides of the rocket stage.
There is a single diamond pattern about 4 stage diameters, or 600 feet, below the F1 engines. What causes this?
- In the F1 the exhaust of the turbo engine is feed to the inside on the wall of the nozle bell. There is a famous slow motion shoot of an Apollo launch where one F1 fills the whole film image, At first we see this dark brown exhaust at the nozle exit and then below comes the bright one from the F1 combustion chamber. By the external expansion at altitude this dark exhaust may be first affected and covers a larger part of the bright one. Then what we see would not be a shock heating but a surface mix of different exhausts.
- Another way for the bright/dark coloration could be flame surface reaction. The F1 burns kerosene in fuel rich mix. The oxygen of the atmosphere could burn up remaining fuel on the surface of the exhaust. The small bright "fingers" on the upper flame cone could be such an afterburn effect.
- Maybe the F1 center engine exhaust has no way to overexpand higher up because it's surrounded by the other engines' exhausts. It would be kept at high pressure for some time until the others had expanded sufficently.
 S-IC/S-II staging
In this photo, the S-IC first stage beginning to separate in a cloud of vapour.
- Just out of curiosity, what causes the exhaust during the S-IC burn phase of the launch to end up engulfing the whole rear end of the vehicle to what appears to be at least halfway up the first stage? I can understand it spreading out due to the decreasing pressure, but what makes it travel forward of the nozzle exit? Was the effect anticipated, or was it a total surprise when it happened the first time? Did it cause any concern about tank integrity? Saturn V exhaust question: ApolloHoax.net
As you say, the exhaust expands in the low pressure of the upper atmosphere. This presents the flow past the vehicle with a large bluff obstruction at the rear end. In the normal manner of fluid flow, it slows down as it approaches the obstruction and the pressure rises. Because of the skin friction along the sides of the vehicle, the air closest to it, the boundary layer, loses energy as it goes aft, and in an adverse pressure gradient it can reach the point where it has zero velocity. This is known as flow separation. From the separation point aft, there are two regions of flow, an outer one with velocity in the original direction and an inner one with circulating flow, moving in the opposite direction along the skin. This is a common situation for flow about bluff objects, but is something you try to avoid in aircraft design as it can lose lift and increase drag, hence the use of streamlined shapes without separation.
In the case of the Saturn V, you have a region of re-circulating flow at the aft end which is essentially like a smoke ring or a doughnut rotating through its hole. This vortical flow mixes with the exhaust at its aft end and brings some of the hot gas forward along the side if the vehicle up to the separation point, then out and back again.
I expect it was anticipated, they certainly did wind-tunnel tests. You can see the same effect on high-altitude photos of the Shuttle and other rockets.
In a typical Saturn V Apollo flight, the five F-1 first stage engines were ignited 6 sec before liftoff. The center F-1 engine was shut down 135 sec after launch and the outer four F-1 engines 15 sec later. One second following cutoff of the four outer F-1 engines, the first stage separated. Simultaneously, eight retrorockets were fired briefly to slow the first stage and prevent it bumping into the second stage. Following separation, the spent first stage fell into the Atlantic about 640 km downrange.
One second after first stage separation, eight solid-fueled motors mounted on the first/second stage adapter ring were fired for 4 sec. As well as maintaining the positive motion of the rocket, this forced the second stage fuel to the bottom of its tanks in order to feed the engines – a so-called ullage maneuver – and was the cue for the five J-2 second stage engines to ignite.
Thirty seconds later, the first/second stage adapter ring fell away, and six seconds after that, the escape tower was jettisoned. The second stage engines burned for 365 sec before the next separation took place.
Four solid-fueled retrorockets on the second stage fired to keep the second and third stages from colliding. Then the second stage began its drop into the Atlantic about 4,000 km from the launch site.
At this point, the Saturn V was traveling about 25,300 km/h at an altitude of 185 km. Two solid-fueled motors on the third stage aft skirt were fired briefly to settle the fuel and simultaneously, the S-IVB third stage J-2 engine fired up for a burn of 142 sec. This initial S-IVB burn carried Apollo into a 190-km orbit at a speed of 28,200 km/h.
The extended missions on the moon required major modifications to the lunar module. Supplies of water, oxygen for the portable life support system, and electrical power were increased. Grumman enlarged the capacity of the propellant tanks by 7% and redesigned the descent stage to make room for the lunar rover. Altogether, the lunar module modifications and the SIM additions added about 2,270 kilograms to the Apollo 15 spacecraft, bringing its total weight to over 48 metric tons.3 This put a burden on Saturn engineers. Marshall and its contractors met the payload increase through minor hardware changes in the S-IC stage and by revising the Saturn V's flight plan. The hardware modifications reduced the number of retrorocket motors, rebored the orifices on the F-1 engines, and set the burning time for the outboard engines nearer LOX depletion. Better use of the Saturn's thrust was achieved by launching the AS-510 rocket in a more southerly direction (changing the launch azimuth limits from 72-96 degrees to 80-100 degrees) and by using an earth parking-orbit of 166 rather than 185 kilometers. Apollo 15 also stood to gain some advantage from the July launch date, when temperature and wind effects would be favorable.4
 S-II separation and burn
The S-II engine burns liquid hydrogen and liquid oxygen, producing a very clean, pure water exhaust: 4H + O2 = 2H2O + lots of energy.
- It looks like we see the smoke of the ignition support solids deflected by the invisible J-2 exhaust bell.
- Could be that, or could perhaps be a shock effect where the J-2 plume meets the surrounding airflow.
The widening of the white lines is less typical for shock interaction here. I checked the location of the interstage solids with the (incomplete) painting sheme of Apollo 11. The GPN-2000-000628 image and its b&w sister are mirrored. S69-39958 and the thread initial KSC-69PC-413 are ok. All seemed to be from the same EC-135N film. Three interstage solids are about the position we see the white lines. One line is in the middle towards the first stage and no longer visible as it goes over it. The two inflight cameras of Apollo 4 got each two of the red/orange solids exhaust in the view too. About the time of S69-39958 the solids were just off.
The two bright dots atop the F1s are residual plumes from the S-IC retrorockets, which were located in the engine fairings, not up top on the upper skirt. 
Note the empty first stage is already slightly tilted.
Perhaps it created a lee wind space at its base where the smoke plume could stay.
The S-IC is blackened by soot from being enveloped in its own exhaust plume earlier. (Many rockets exhibit such backflow at high altitudes, but it's a lot more conspicuous with the Saturn V.)
These photos were taken with a 70mm Airborne Lightweight Optical Tracking System (ALOTS) camera on a U.S. Air Force EC-135N aircraft. The 20 foot long, 5 foot diameter camera pod was mounted on the cargo door at the side of the aircraft.
NASA modified eight KC-135N jet aircraft in the mid-1960s to provide telemetry acquisition, vehicle tracking and two-way voice relay between manned Apollo missions and mission control in Houston. The interior was configured to contain all the necessary electronic support equipment. Four of the aircraft were also modified to use an ALOTS pod.
The ARIA (Apollo Range Instrumented Aircraft) aircraft were designed to deploy around the world, especially in those areas where no ground-based telemetry and tracking facilities were available. They were also used to assist in locating the Apollo command module following splashdown.
The most noteworthy feature of the ARIA aircraft was the huge, rounded nose, modified to house a 7-foot diameter S-band tracking antenna dish. Because of this unique feature, the ARIA aircraft had a number of nicknames, including "snoopy", "bulbous", "hog nose", and "the nose that goes".
- ↑ 1.0 1.1 1.2 Various authors, EC-135N still images?, sci.space.history, January 2006
- ↑ User gwiz, Cornwall, Saturn V exhaust question, ApolloHoax.net forums :: The Reality of Apollo :: Saturn V exhaust question, May 15, 2006
- ↑ Charles D. Benson and William Barnaby Faherty, A Change of Course for Apollo, Moonport: A History of Apollo Launch Facilities and Operations, Chapter 23-1 Extended Lunar Exploration: Apollo 15-17, NASA Special Publication-4204 in the NASA History Series, 1978.