# Mini Series: Designing a Satellite for Dummies

Are you an aspiring aerospace engineer, a space enthusiast, a parent checking your child’s homework or simply interested in the specifics of how to design certain satellite parts? Then this is the place to be.

In this mini series we will go through the basics of designing and scaling a satellite, ranging from solar arrays to propellant tanks and even orbital parameters. If you would like us to cover other space-related topics, feel free to reach out to engineering@valispace.com.

## Part 4: How to Size an Attitude Control System

In the last tutorial we showed you how to calculate the different disturbance torques acting on a satellite. In this tutorial, we will show you how the Attitude Determination and Control System (ADCS) copes with these torques. As a starting note, there are a lot of ways to do this! Thrusters, reaction and momentum wheels, control moment gyroscopes and magnetic torquers are examples of devices that can handle these torques. We will provide you with knowledge about one of the more simple ways to do this, namely by using either momentum or reaction wheels (not both!) to provide attitude control and then using thrusters to desaturate the wheels. This setup is quite common as reaction and momentum wheels are both proven and simple concepts which perform well over a wide range of missions. Thrusters are a good choice as they can also be used to provide orbit control, for instance to de-orbit the satellite at its end of life. Note that this is just one way to do it and not necessarily the best one, but it should give you a good idea of the overall engineering process!

### Actuators

The ADCS actuators are used to counterbalance, either continuously or re-actively, torques generated across the spacecraft by any manner of disturbances. In the following we will show you how to size the reaction and momentum wheels and leave the choice of which one to pick up to you.

#### Reaction wheels

A reaction wheel is a type of flywheel used for three-axis attitude control. It provides a high pointing accuracy and is particularly useful when the spacecraft must be rotated by very small increments, such as keeping a telescope pointed towards a star. In general there are two main drivers for the sizing of the reaction wheels, the maximum required torque and the required momentum storage.

##### Required torque

The maximum required torque can either be any of the disturbance torques scaled with a margin (generally of around 1.25) or the slew torque. Slew torque describes the torque required to slew (or rotate) the spacecraft across an angle in a specific time. The amount of slew torque required changes significantly per type of mission, for instance smaller Earth observation satellites will generally not require any major slews while bigger ones (e.g. espionage) do. If a lot, or faster, slew maneuvers are required, it might also be interesting to take a look at control moment gyroscopes!

To calculate the slew torque, use the following equation:

$$T_{slew} = 4 \theta \frac{I}{t^2} \; \; [Nm]$$

Where $\theta$ is the required slew angle in radians, $I$ is the total moment of inertia of the satellite and $t$ is the time in which the slew maneuvers must be performed. Now, the torque requirement is either 1.25 times the maximum disturbance torque $T_D$ or the slew torque, whichever is higher.

##### Required momentum storage

To estimate the required momentum storage we can integrate the worst-case disturbance torque over one full orbit. If either the gravity gradient, the solar radiation pressure or the aerodynamic torque is the maximum disturbance torque, the required momentum storage can be approximated to build up in one quarter of an orbit and is then equal to:

$$h = T_D \frac{P}{4} (0.707) \; \; [Nms]$$

Where P is the period of the satellite’s orbit. Normally, the magnetic field torque can be assumed to not build up the highest momentum as it is highly variable. If you do want to calculate it, check these sources.

##### Sizing the reaction wheels

Now that we know the maximum required torque and momentum storage, it is time to find the required size of the reaction wheels. It is common to use a set of 3 wheels, with their spin axis not co-planar, to provide three-axis attitude control. To provide redundancy in the design, often a fourth is added. This fourth wheel however will not be placed orthogonal, which means that a higher torque and momentum will be required. In satellite design, it is common to select off-the-shelf reaction wheels, because the reduction of mission cost and risk normally weighs up to the reduction in mass which you achieve when you design them yourselves. To find the optimal reaction wheel, simply select the reaction wheel that is most suitable for your torque and momentum storage requirements, for instance on the Satsearch shop. Remember, if you are using Valispace, you can simply import them from the Satellite Catalog!

#### Momentum wheels

Next to reaction wheels, momentum wheels are commonly used to counter disturbance torques. A momentum wheel is always spinning at a high speed, making the spacecraft more stable. This means the spacecraft is more resistant to changing its attitude by exploiting gyroscopic affects. This is ideal for spacecrafts that aim to maintain a fixed attitude with respect to a point in space (e.g. the Earth) while undergoing continuous disturbance torques. The momentum storage required is as follows:

$$h = \frac{T}{4} \frac{T_D}{\theta_a} \; \; [Nms]$$

Here, $T$ is the satellite’s orbital period, $T_D$ is the maximum calculated disturbance torque and $\theta_a$ is the allowable motion. Check your satellite’s pointing requirements to find this maximum allowed angle!

Now, the process to find the most suitable momentum wheel is the same as for the reaction wheels. Give this website a look!

#### Choosing your actuator

By now, we have found the requirements for both reaction and momentum wheels. By looking up some appropriate components and comparing them for mass and size, you should be able to find the best one!

### Momentum dump

Both reaction and momentum wheels build up momentum periodically. This momentum needs to be dumped to keep these wheels operational. For this, thrusters are an excellent choice (also for large slewing maneuvers if these are envisioned in your satellite mission). Thrusters may also be used instead of reaction and momentum wheels to counteract disturbance torques, however this scenario is inefficient due to the extremely small torques required. Because these torques are small, the required thrust from the thrusters is also small, and these small thrust forces are hard to create and maintain throughout the spacecraft’s life.

It is necessary to choose thrusters powerful enough to counteract stored momentum and to place them strategically across the vehicle. One good way to do this is giving the satellite a set of fully redundant thrusters for each axis (for instance 2*2 per 3 axes for a total of 12).

#### Force required

In order to de-saturate a reaction or momentum wheel we assess the maximum force required. The equation for this is as follows:

$$ F = \frac{h}{Lt} \; \; [N]$$

In here, $h$ is the stored momentum, $L$ is the moment arm in meters (so the distance from the center of gravity to the location of your thrusters) and $t$ is the burn time of the thruster, which can be assumed to be $1 \; [s]$, but can also be any other appropriate value.

#### Thruster choice

There are many different combinations of thrusters and propellants that can be used in the ADCS. Typical values can be found in reference tables, which can for instance be found in SMAD or other sources. The choice for which type of thruster and propellant to go depends on a lot of factors. Namely the $I_sp$ of the thruster, the mass, minimum burn time and the total impulse. Finally, always make sure that the thrust is higher than the required thrust! To learn more about which thrusters are available on the market and how to pick one, check out this article on cubesat thrusters.

#### Propellant mass

To determine the propellant mass required is simple. We simply need to know the total impulse imparted on the satellite during its lifetime (I_t), the force required per pulse, calculated above (F), the $I_sp$ and the gravitational acceleration of the Earth (g_E):

$$M_p = \frac{I_t F}{I_{sp}g_E} \; \; [kg]$$

The total impulse can be estimated to be:

$$I_t = t_{pulse} N_{wheels} L_{days} \; \; [Ns]$$

In here, $t_{pulse}$ is the time per pulse, N_{wheels} is the number of wheels being used per day (normally 3) and L_{days} is the lifetime of the satellite in days.

If you followed the steps correctly, you have now sized your own attitude control system, congratulations! Note that for a fully functioning ADCS, you also need sensors to measure the attitude!

*We hope you liked this mini-tutorial! If you want to learn how ADCS is related to other subsystems in a satellite or how to design a complete satellite using Valispace and practical examples, also check our **Satellite Tutorial**. Stay tuned for more and feel free to give us feedback at *contact-us@valispace.com!

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