Tag Archives: calculation

Rocket Science

My son, my wife and I have been messing around with model rockets. They seem to be a big thing in the USA, but are a lot less common here in the UK. They are a lot of fun.

I bought the above rocket + launch pad + launch controller kit from a local model shop, with some recovery wadding and 3 class C rocket motors with igniters:

rocket kit amazon.co.uk link

rocket kit amazon.com link

The total cost was £30.

Making the rocket involved a bit of glueing and assembly, but was fairly straightforward. Then we inserted some wadding (to protect the internals from the hot gas of the rocket motor), the recovery parachute and the nose cone with rotors. When it was finished we took it to a big open space, inserted a rocket motor and igniter, put it on the launch pad and used the 9v battery operated remote control to launch it.

We had a few non-launches because the crocodile clips (connecting the launch control to the igniter) touched, causing a short-circuit, or fell off. Not a great design. Once we had sorted that out we successfully launched and the rocket went well over 100 metres in the air. Cool!

In theory the motor should burn for a couple of seconds and then a little explosive charge fires to separate the nose cone from the main body. The main body then floats down on the parachute while the nose cone deploys spring-loaded rotors and auto-rotates down. In theory.  However, in our inexperience, we put in too much wadding and packed it too tightly. Consequently the rocket blew itself apart in mid-air and the parachute and rotors didn’t deploy. We managed to recover all the bits. The parachute was ok, but the rotor blades were too damaged to use again.

A video of our first launch

So we cut off the damaged section and added the nose cone back on to make a new, shorter rocket and did 2 more launches. Being lighter with the same motor it went a lot higher. Possibly over 200 metres!

We made a new rocket from the nose cone and tail of the kit, plus a long cardboard tube and lots of duct tape. We did another 3 launches using C class rocket motors. Even managing to get one successful parachute deployment. However as the new rocket was  heavier it got noticeablely less height, probably less than 100 metres.

A few things we learnt along the way:

  • Don’t force the parachute and nose cone in too hard or use too much wadding.
  • If the parachute doesn’t deploy the rocket can survive hitting the ground at speed surprisingly well. But they make quite a hole in the ground, so you REALLY don’t want to get in the way.
  • Even in light wind the rockets can land a fair distance away. Especially if the parachute deploys successfully. So pick a still day for the launch. You can also cut some extra vents in the parachute to make it fall faster.
  • You need a BIG open space, free from other people, animals and trees. Preferably at least 200 metres across, if you want to stand a good chance of recovering your rocket for another launch.
  • The maximum height of your rocket depends critically on the thrust to weight ratio.

Hopefully it goes without saying that pyrotechnics and objects travelling at high speed are potentially dangerous and require common sense and adult supervision.

Being a software geek with a physics background I couldn’t resist doing a few calculations. Here is a little Python script I wrote to calculate the maximum height and flight time based on the mass of the rocket and the thrust and duration of the motor. It applies a simple time-step approach to F=ma. Just modify the mass, thrust and duration variables.

rocket science codeIt assumes the rocket goes straight up and doesn’t allow for air resistance. But the values it calculates seem fairly plausible based on my observations. You can get the code via this link:

Python rocket calculation code

For example with a thrust of 6N for 1.6s I calculate a maximum height of:

Mass (Kg) Max height (Metres)
0.1 388
0.15 156
0.2 78
0.25 43

So you can see how critically important thrust to weight ratio is to maximum height.

Presumably it is possible to derive an analytic solution as well. I leave that as an exercise for the interested reader. ;0)

I think we will try a D-class motor next time (each step up the alphabet doubles the impulse). This seems to be the biggest that you can get hold of in the UK without a license. Watch out passing aircraft.

To infinity and beyond!

Calculating volume discounts for software

discount.jpgIf people buy your software in bulk they expect to get a discount. But how much of a discount should you give them? A simple formula I have seen used is:

discounted price = unit price * n^f

Where n is the total number of units purchased and f is a scaling factor between 0 and 1. So, for example, if my unit price is 24.95 (pounds, dollars etc) and f is 0.8, the discounted price for 10 units is = 24.95 * 10^0.8 = 157.42, which you can then round to a more aesthetically appealing number.

This is a little over-simplistic, as it doesn’t take account of the cost to you of each unit (for example the duplication and postage cost of CDs and the cost of payment processing). We can get around this by breaking the price into a fixed cost and a margin and only applying the discount to the margin. Below is a link to a simple Excel spreadsheet that does this for you. You can change any of the values in the orange fields. f seems to give sensible results in the range 0.75 to 0.9.

discount_spreadsheet1.png

discount spreadsheet (29kb, Excel 97-2003 format)

This spreadsheet can be useful to give you a starting point, but you also need to consider what the customer is prepared to pay. You maximise your profit by giving the buyer the minimum discount that is required to make the sale. For example, a reseller is out to make a profit and will probably expect a bigger discount on the same number of units than a large company buying in bulk for their end users. When in doubt, reduce the discount. You can always increase it a bit later if they don’t buy.