Tag Archives: model

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!

Should I give free upgrades for life?

There are any number of different licensing models. For commercial software the main ones are:

  1. subscription
  2. outright purchase, with annual maintenance
  3. outright purchase, with free minor upgrades and paid major upgrades
  4. outright purchase, with free major and minor upgrades for life

Subscription payments and purchase + maintenance are nice, if you can get them. They give a more predictable cash flow for a business and you can generally charge a higher lifetime price than you can with a single payment. But this isn’t appropriate for all types of software. For example, it doesn’t make much sense for lower priced desktop software. Assuming subscription or purchase+maintenance isn’t an option, the question boils down to – should we charge for major upgrades?

Let’s look at the numbers for a simple (contrived) example. AcmeSoft sells 1000 licences of v1 of their product in year 1, 2000 licences of v2 of their product in year 2, 3000 licences of v3 of their product in year 3 etc. Each year 50% of the customers who bought the previous version (new or as an upgrade) pay to upgrade to the latest version. The upgrade costs them 50% of the initial purchase. How much is the upgrade revenue worth? We can create a simple model in Excel:

Income new licences (blue) vs income from upgrades (red). Click to enlarge.

Percentage of annual income from upgrades. Click to enlarge.

In year 8 the upgrade income is actually worth more the new licence income. By year 10 upgrades are worth some 60% of yearly income for the product. If the product has a 10 year lifespan, nearly 50% of the total income from the product will be from upgrades. So it only makes commercial sense to give free upgrades for life if this will at least double the conversion ratio[1]. This seems highly unlikely. You can always try changing your upgrade policy and measure what effect it has on your conversion rate. Not much, I would guess (if anyone has tried it, I would be interested to know the results).

Even in a more pessimistic model where only 30% of customers upgrade and they only pay 30% of the new licence fee, upgrades still account for nearly 25% of total income over 10 years. You can download the spreadsheet and play with the parameters yourself.

Upgrade income becomes particularly important when:

  • A product has a long life span.
  • Customers are very likely to upgrade to a new version.
  • There is little growth in new sales.

In the worst case you could end up with a product with a huge customer base built up over a long period, but which makes very few new sales as it has saturated the market. Free major upgrades would mean that each major release is then going to result in large expense (developent and support) but very little income. Microsoft must be very happy they didn’t offer free upgrades for life on Windows or Office!

I don’t see anything unreasonable about charging for major upgrades. The vendor has to do additional work to add the new features and existing customers can choose whether the new features are worth the upgrade fee. However customers have certain (not unreasonable) expectations for paid upgrades:

  • The fact that the customer is expected to pay for major upgrades needs to be made clear before purchase.
  • Any major bugs in version n should be fixed before releasing version n+1.
  • A major upgrade should have significant new features.
  • Major upgrades should not be released more than once every 12 months.
  • The upgrade fee should be reasonable. Around 40% of the cost of a new licence seems typical.
  • There should be a grace period for free upgrades. E.g. If I buy v1 of a product on 01-Jan I don’t expect to have to pay an upgrade fee for v2 released on 02-Jan. Typically this grace period is 3-6 months.

If you are offering free upgrades for life currently, you can change your policy to paid major upgrades. But, obviously, you will need to honour free upgrades for everyone who purchases before the change of policy.

There are some, apparently successful, companies that offer free upgrades for life (Axialis for example). But I have heard many tales of small software vendors regretting their initial decision to give free upgrades for life. The easiest customer to sell to is the one you already have. If you don’t charge for major upgrades, are you leaving large amounts of money on the table?

[1]Ignoring inflation, interest etc.