A Little About OCO Mission’s Failure
March 13, 2009
On February 24, 2009, Orbiting Carbon Observatory (OCO) spacecraft failed to reach its orbit at 705 km above the earth due to rocket malfunction.
The fairing covering OCO spacecraft on top of Taurus XL rocket apparently did not separate as planned, officials report said it so far.
John Brunschwyler, Taurus program manager from Orbital Sciences, said: “The fairing has considerable weight relative to the portion of the vehicle that’s flying. So when it separates off, you get a jump in acceleration. We did not have that jump in acceleration.”
“As a direct result of carrying that extra weight, we could not make orbit.”
In this post I won’t write about why this incident happened, but I am trying to discuss about how the failed-to-be-opened clam shell fairing affects the entire mission so it failed to get into orbit.
As Mr. Brunschwyler said, the rocket carried an extra weight because the fairing failed to separate and that lead to orbit insersion failure.
Now we know that weight is a major factor in orbital flight mission, along with the value of engine specific impulse (Isp) it takes an important part to produce velocity that a spacecraft will achieve.
Tsiolkovsky’s Equation dictated , with mo is the initial mass, m1 is the final mass and ve is the effective exhaust velocity (ve = gravity force / Isp).
The output of the equation is the velocity increment achieved by a spacecraft. First, we need to predict the velocity needed to circle around the earth. (note: when you know the required velocity, you will get the required propellant mass and the allowable weight.)
OCO spacecraft was planned to fly around the earth with a circle shape trajectory in the altitude of 705 km above earth sea-level. According to vis-viva integral equation , the required velocity to circle around the earth in OCO’s altitude is around 7.505 km/sec. That is the ideal velocity needed. In the actual flight, rocket will experiencing a number of forces and moments that will affect its flight, including aerodynamic forces and moments, thrust mis-alignment, body rotation, earth rotation, etc.
Now we know the required final velocity for the entire mission. But to understand the effect of fairing weight to the mission, we only need the velocity increment in TaurusXL final stage.
I don’t get the OCO-TaurusXL rocket’s actual data yet, only the data of previous Taurus rocket (www.astronautix.com), but I think that’s enough to do some rough analysis.
I found that the weight of TaurusXL fairing is around 1400 kg -yeah that’s quite heavy, but it’s acceptable according to the function of protecting rocket payload from heat and other external disturbance.
How much is that 1400 kg affect the velocity?
My analysis using the Tsiolkovsky’s Equation found that if the fairing was separated, the final stage rocket will give around 1.7 km/sec to the total velocity increment.
And if the fairing was not separated from the vehicle, the final stage rocket will only give around 0.8 km/sec to the total velocity increment -that is just the half of what it should be.
So if your launch vehicle was planned to reach 7.5 km/sec, it will only reach around 6.7 km/sec because of the fairing is still attached. And yes, your spacecraft will do the sub-orbital trajectory and fly back to the earth.
I believe that is quite near to what’s occured in the OCO-TaurusXL flight operation.
Note: The pictures of TaurusXL was taken from nasaspaceflight.com, news.bbc.co.uk and floridatoday.com