If a Saturn V rocket were held down by four bolts, how thick would the bolts have to be to hold it down?

Question

Apollo mission rocket. Imagine 4 bolts holding it down during launch. Forget the fact that they would probably melt.

Answer 1

In addition to a safety factor, and the rising thrust due to the use of fuel while the rocket is held, you'd better also figure the characteristics at some VERY high temperatures. Given that the temperature on the bolts would rise swiftly, and would also probably vary noticeably down the length of the bolt due to the bolt being bolted to something that would certainly shield the lower portions from direct exhaust heat, it seems likely you'll be doing calculus to solve this one. For that matter, what are the heat transfer characteristics of the material the bolts bolt to? How are they threaded? What would the characteristics of the nuts need to be? There will be a trade-off available between the nuts and the bolts. Frankly, I'd think of welding the assembly as a further safety margin.

I don't know the answers, of course, but I'm thinking the bolts are bigger by a fair margin than 3-4 inches.

Answer 2

The Saturn V rocket develops a thrust of 7.5 million pounds, = 7,500,000 lb at launch, and weighs 2700 ton= 5,400,000 pounds.

So, the initial thrust is 2,100,000 lb greater than the weight.

The load on each of four anchor bolts would be 525,000 lb.

Assuming a high strength ASTM A490 anchor bolt with an allowable stress of 54,000 psi, the bolt size would have to be 525,000/54,000 = 9.72 sq. in. which would require a 3.52 inch diamater bolt, which would probably melt.

Also, as the fuel is used up the weight would decrease, but we do do not have any data for thrust reduction as the fuel is used, so if the fuel weight decreases faster than the thrust, the bolt area required would increase.

A 3 3/4 " diameter ancor bolt is not unheard of. Many of our Cracking towers and flare stacks had anchor bolts this large or larger.

Answer 3

Don't forget to build in a safety factor into your calculation to account for metallurgical weaknesses in the bolts. Actually, some of the Apollo rockets were held on the launch pad by bolts or clamps to build up max takeoff power before releasing or exploding.

Answer 4

Assuming the bolts were perpendicular to the ground and the rocket was shooting straight up, also that the force is evenly distributed to each of the bolts, and evenly distributed throughout the cross-section of each bolt:
Find the upward force of the rocket, as well as the maximum tensile stress allowed for the bolts. The formula is: max tensile stress=Force of rocket/ Total cross-sectional area of the bolts. Solve this for the diameter of the bolts.