Wednesday, 27 October 2010

Gathering more information on the problem of How to Stop BLOODHOUND?

Last week I introduced a vague initial problem statement for how to stop BLOODHOUND, and asked for comments on what questions I should ask John Davis to start gathering more information.

On Twitter, @printerelf, an aerospace engineer, suggested a couple of good questions. He asked
Q1. How much KE (Kinetic Energy) will the car have when the chutes are deployed?
Q2. How big are the parachutes?

Let's take these questions in turn. Firstly, the definition of kinetic energy is 0.5*mass*velocity2, therefore, in order to know the kinetic energy of BLOODHOUND, we need to know its mass and velocity. We can look up that the mass of the car plus the driver Andy Green (once the fuel has burnt off) will be approximately 5000 kg, with more details available from However, the velocity of the car when the chutes are deployed is unknown, in fact, the velocities can be thought of as design parameters that we can adjust to find the best way of stopping BLOODHOUND. Hence, after a bit of thought, we see that Q1 is just an alternative way of phrasing the part of the initial problem (i.e. where to place the markers around the Speedo to give Andy guidance of when to deploy the parachutes)

Re-phrasing vaguely worded problems can often help to understand the problem better, or to suggest possible routes to a solution. In this casethe thought of looking at the problem from an energy perspective strikes me as a promising one. It prompts me to recall that many physics-related problems can be solved through applying the laws of conservation of energy, and indeed in a recent phone call with John, he'd mentioned that an energy-based analysis may be relevant. We should keep this inkling in mind as we explore the problem further.  

Q2 is also pertinent. The size of the parachutes will relate to the amount of drag (the force acting to slow down BLOODHOUND): the bigger the area of the parachute, the larger the drag. However, the parachute size isn't known as the supplier for the parachutes hasn't been fixed yet. This is another typical feature of real-world problems - the numbers used in the calculations change as the project progresses. For now, John tells me we should use a 'D/q value' (also known as a drag coefficient) of 0.8 for both parachutes. I remind myself (using a spreadsheet Ron Ayers once gave me) that it is common in aerodynamics to model drag as the product of the drag coefficient 'D/q' and q, the dynamic pressure, i.e. DragChute = 0.8*q. Here, DragChute is the drag force from the chute in Newtons (N), and q is the dynamic pressure in m2
Both @printerelf's questions revealed more information about the problem in hand. What other questions might you want to ask at this stage? Suggestions welcome in the comments below. 

The first questions I actually asked John reflected my background as a mathematician and were aimed at trying to cast the problem as the solution to an optimization problem. I asked: 
What is the objective of the choice of chute opening times? E.g. Is it to stop at exactly 10 miles, or for them to open at defined speeds? What constraints apply? 
Tune in next week for John's reply...  

Wednesday, 20 October 2010

Initial Problem Statement - How to Stop BLOODHOUND?

Here is the initial problem statement in the first email I received from John Davis on this topic.

On the slow down from the high speed runs it is important that the staging of the parachutes and wheel brakes ensure that the car is brought to a halt by the end of the 10 mile track.

Andy is keen to have markers around the Speedo which gives him guidance of when to deploy the parachutes, Chute 1 then Chute 2. These pointers need to be dynamic and automatically adjust should the previous one be late or less efficient than expected.

The basic mathematics is based around a simple Drag/Mass equals Acceleration model with the Airbrakes and Chutes having an assumed Drag Coefficient.

What I need is some simple equations to put into the Simulink Code to work out the required speed at which the next deployment is required.

If you feel you have some time to help I would like to talk through the information that is required to complete this model.
This is a typical introduction to a real-world problem. Unlike word problems you may remember from maths class in school, the problem is ill-defined, no numbers are included, and much more detail is needed before the 'simple equations' can be identified.

However, what the email does convey is:
  • It is a problem worth solving
  • The customer for the solution is defined: Andy Green the pilot/driver
  • A qualitative description of what is needed: simple equations and dynamic speed markers
  • Pointers to the mathematics/physics that will be needed: aerodynamics and Newton's 2nd law of motion 
  • The software for implementing the equations will be Simulink  
  • John is starting the problem-solving process by figuring out who can help him solve it  
How would you respond to the email? What questions would you ask? Suggestions in the comments below....

Monday, 18 October 2010

First Blog - An Introduction

Well, here goes with my first personal blog post. The blogging impetus came from a conversation I just had with Dr John Davis, Senior Controls System Engineer for the Bloodhound Super Sonic Car. Bloodhound aims to go 1000 mph and in the process inspire the next generation of scientists, engineers and mathematicians.

John asked for my help to solve the problem of when and if to use the parachutes in order to decelerate Bloodhound from > 1000 mph at the end of the measured mile to stop exactly at the 10 mile marker. Rather than just solve the problem and then document a neatly packaged answer, we are hoping to open up our thinking process in order to give students and Bloodhound enthusiasts an insight into how 'real-world' engineering problem-solving works.  I'll be posting regular updates on our progress. Perhaps we may end up crowd-sourcing an even better solution through the comments!

By way of introduction, I am the Application Engineering Manager at MathWorks in the UK. The MathWorks tools are being used for several elements of the design of Bloodhound, including the control system and aerodynamics. I plan to write this blog during the remainder of my maternity leave and any views expressed are my own. You can follow me @tanyammorton and the Bloodhound project @bloodhound_ssc on Twitter. The hashtag for the problem is #stopbloodhound.