Looking for an example.... (misalignment of the Apollo 11 rocket)

[Bigbad]

TL;DR Summary

How off would the Apollo rocket needed to have been off for the moon landing to not have happened?

I once read that if the Apollo 11 rocket had been misaligned by even half a degree on the launch pad that the lunar landing would not have happened. I would like to find this information again to use it as an example for my students in their life planning, i.e. if they make small mistakes now it may have big consequences in the future. Does anyone remember what this number was?

 

[Dale]

Summary:: How off would the Apollo rocket needed to have been off for the moon landing to not have happened?

I once read that if the Apollo 11 rocket had been misaligned by even half a degree on the launch pad that the lunar landing would not have happened.

I don’t know the source, but it is not correct. A rocket does many course corrections and adjustments over its mission. Half a degree on takeoff would simply be corrected just like any deviation due to early atmospheric turbulence.

A better lesson might be the need to constantly monitor where you are and your path and to continually make small corrections.

 

[Halc]

A gust of wind could have done that. Surely the Saturn-V had the capability of minor course corrections while getting itself into orbit. Half a degree tilt while at rest on the launch pad would have moved the top of the rocket over by a meter which would probably have resulted in an inability for the top arm of the tower to align properly with the crew hatch. I think they'd fix something like that before firing the thing off, so no lunar mission failure there.

Problems at launch time might affect the ability to launch into orbit, but the moon mission is still on if it makes it into orbit without further issues.

 

[anorlunda]

I would like to find this information again to use it as an example for my students in their life planning, i.e. if they make small mistakes now it may have big consequences in the future.

If that is the point, I would use Robert Frost's poem, The Road Not Taken.

 

[Bigbad]

Thank you! I am old :( What about a more simple rocket - only the one stage? without a guidance system? These are 6th graders...they like things that go boom. Robert Frost is awesome, but their appreciation for philosophy has not yet developed :)

 

[Dale]

How about the big guns on a large naval battleship?

 

[ardnog]

How about the big guns on a large naval battleship?

source: http://navweaps.com/Weapons/WNUS_16-50_mk7.php

 

[ardnog]

Another thing you can teach, you have to compensate for the Coriolis force (rotation of the Earth) when aiming at these ranges. At least you would, today, to achieve modern accuracy numbers.

 

[PeroK]

I would like to find this information again to use it as an example for my students in their life planning, i.e. if they make small mistakes now it may have big consequences in the future.

What a terrible thing to teach children! You fail an exam at age seven and your life is ruined?

 

[Arjan82]

Due to the rotation of the Earth a severe constraint in launch angle equals a very narrow launch window (timewise). Since the launch window was a few hours this is not at all a problem. Not to say that there was an 'earth parking orbit' which they would stay in for a while before launching themselves towards the moon. I presume the launch from Earth orbit towards the moon needs to be accurate however (but again: they make corrections during the entire trip, based on star navigation I believe).

But I also strongly agree with @PeroK actually. It is very scary to me (and I presume also to a child) to learn that if you make even a small mistake now, it might have a massive effect on your entire life. I don't think that is true at all. You have the possibility to do many corrections. And on the other hand, sometimes life takes its own path, out of your control, than you just have to wing it .

As the wise lyrics of a Dutch song (Acda en de Munnik - Laat me slapen, about the murder on John Lennon):
" Life is whatever happens, while making other plans"

 

[russ_watters]

I don't see that anyone pointed out that rockets launch vertically because otherwise they'd fall over when sitting on the launch pad. That's nowhere close to the direction they need to be pointed to get where they are trying to go, nor is the attitude constant. Ultimately the early flight path is a spiral that ends up closer to horizontal than vertical.

 

[ardnog]

With some smaller rockets they can be launched at an angle. But sometimes you don't want to do this as you want to take the shortest (or otherwise optimal for whatever reason) path though the thickest part of the atmoshere into space.

Edited for clarity.

 

[256bits]

if they make small mistakes now it may have big consequences in the future.

How small, or big, a mistake?

Is this an attempt of applying the misunderstood 'butterfly effect' to humans?
https://science.howstuffworks.com/math-concepts/butterfly-effect.htm

Human human behavior is probably better modeled with some sort of application of chaos theory, where direct cause and effect is somewhat foggy.
https://en.wikipedia.org/wiki/Chaos_theory

 

[russ_watters]

How small, or big, a mistake?

Is this an attempt of applying the misunderstood 'butterfly effect' to humans?

Probably not. It's probably just a really bad attempt to describe how exact the trajectory has to be. Here's an Apollo 13 movie quote of the type of thing people say about such things:

In order to enter the atmosphere safely, the crew must aim
for a corridor just two and a half degrees wide. If they're
too steep, they will incinerate in the steadily thickening
air, if they're too shallow, they'll ricochet off the
atmosphere like a rock skipping off a pond. The re-entry
corridor is in fact so narrow, that if this basketball were
the earth, and this softball were the moon, and the two were
placed fourteen feet apart, the crew would have to hit a
target no thicker than this piece of paper.

What is sometimes missed in these descriptions is the fact that (of course) the tolerances are well known, the capabilities of the controls are well known, and so course corrections are pre-planned/built-in to the trip. So while it sounds like a tough/risky proposition that you have to be so exact, it's really not.

That's for ballistic return and re-entry, where the engines are off almost the entire time (and discarded). For launch, none of this really applies since the rocket is under full/active control the entire time until reaching Earth orbit. And, of course, going from Earth orbit to lunar orbit is a separate burn.

 

[Ibix]

Perhaps a useful life lesson, though, is that small course corrections early have a lot more impact than similar interventions later on. I've heard that kind of ongoing active control of projects called "fail early, fail often", although kids may not appreciate the irony in that.

 

[Andy Resnick]

[...] and so course corrections are pre-planned/built-in to the trip. [...]

(mumbles something aobut imperial/metric units and the Mars Climate Observer)

 

[256bits]

they'll ricochet off the
atmosphere like a rock skipping off a pond

.
...and return sometime later back to Earth to try again.

Problem is, with the second attempt, by that time, their oxygen supply has run out.

 

[Frabjous]

As described above, this is a non-applicable calculation, but here is the origin of the number
R, radius moon 1080 miles
D, distance Earth to moon 238900 miles
arctan(R/D)=arctan(4.5e-3)=.26 degrees
Multiply by 2 to get angle subtended by moon 0.52 degrees

 

[A.T.]

These are 6th graders...they like things that go boom.

Maybe use things that go boom as analogy for something else, than their lives.

What about a more simple rocket - only the one stage? without a guidance system?

This is not how life works.

 

[ardnog]

I'm sure the main problem with aiming at the moon isn't the accuracy of the calculation (which is, obviously, school stuff) but the lag in the controls and the precision of the rocket's engines and sensors. I think it's like playing video games with a dodgy controller over a lagged connection.

 

[sophiecentaur]

What a terrible thing to teach children! You fail an exam at age seven and your life is ruined?

That's particularly relevant in a time of Covid. You have to have faith in the constant possibility of redemption.
Our lives and the progress of life in general rely on negative feedback.