Weight

Weight is one of the three forces on a rocket seen in the rocket image below. Weight is the force generated on the rocket by the gravitational attraction of the earth. It is the combined mass of the rocket itself, including the fuel, and the payload, multiplied by the gravitational pull from earth. As shown in the rocket image below, weight opposes thrust - one of the other forces of flight. Weight pulls vertically downward through the rocket's center of gravity (CG). Center of gravity will be explained in more detail in the stability section.

We all have our own body weight, and can weigh ourselves on a bathroom scale. So weight should be a familiar concept. We can also determine when one object is heavier than another by picking up both objects - whichever object takes more effort to pick up, is usually the heavier object.

One of the elements of weight is the gravitational force from the earth. This gravitational force is fundamentally different from the aerodynamic forces of lift and drag. Lift and drag are mechanical forces, meaning the rocket has to be in physical contact with the air to generate the force. However, a gravitational force is a field force. A field force means that two objects do not need to be in physical contact to generate a force between them. The earth does not need to be in physical contact with the rocket to generate the gravitational force. Isaac Newton expressed the relationship between weight, mass, and gravitational pull in a single equation:

Since gravity is strongest on the surface of the earth, the gravitational attraction between an object (let's say a rocket) and the earth weakens as the rocket rises up in altitude. However, knowing that gravity is relatively constant at 9.8 m/s² allows for the relationship in the chart below. As mass increases by 1 unit, weight will increase by 9.8 units. This is due to mass being multiplied by gravity and the result is an object's weight.

Note: A newton is the metric unit for force. One newton is the force required to accelerate a mass of one kilogram to one meter per second squared.

The weight of a rocket is always directed towards the center of the earth. The amount of weight first depends on the mass of the rocket itself. Mass is a measure of the amount of matter or material an object contains. For a rocket, the total mass would include the mass of the rocket itself, fuel, and any additional payload on board. Mass and weight are directly proportional, so increasing mass will also increase weight. But as the formula for weight shows, mass and weight are not the same. Weight takes into account the gravitational pull on the mass. A rocket, for example, would weigh less on the moon than it does on the earth, even though the mass of the rocket would remain the same. How is this possible? The moon is quite a bit smaller than the earth - about 1/4 the earth's size. This means that gravity is lower on the moon - about 1.64 m/s².

To determine the weight of an object, we first need to know its mass. The equation for mass is:

As the formula indicates, you can alter the mass and ultimately the weight of your rocket by either changing density or volume. Since density is a material property, you change density by using different materials. Using materials that have a higher density will result in higher mass (and weight). Likewise materials with a lower mass will help you reduce the mass (and weight) of your rocket. The following table lists a few fin materials and their density.

The equation for mass also shows us that we can change mass and weight by changing volume. The volume is the size and amount of material that you use to build the rocket. If you increase volume, mass (and weight) will also increase. Mass is directly proportional to density and volume.

The following table summarizes the independent variables that affect weight. To make the concept of weight actionable it is important to have a good understanding of which variables you can control and how you want to control them.

Variable	Can you control this variable?	How is the variable controlled?
Gravity	No	Gravity is a constant (9.8 m/s2)
Density	Yes	Density is a material property, so you control density by the materials you choose.
Volume	Yes	Volume depends on the size and shape of the rocket components you design and select.

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Calculating Weight

Let's calculate the mass of two different rocket fins to see the impact of density and volume on mass. Using the chart from above, the density of card stock #2 is 0.754 g/cm³. Assuming the fin of your rocket has a size of 0.1864 cm x 5.08 cm x 10.16 cm, to calculate the mass we need to first calculate the volume:

Step 1	Write out equation for volume	volume = thickness x width x length
Step 2	Fill in the variables you know	volume = 0.1864 cm x 5.08 cm x 10.16 cm
Step 3	Calculate volume by combining terms (don't forget units)	volume = 9.62 cm3

Next we would calculate the mass:

Step 1	Write out equation for mass	mass = density x volume
Step 2	Fill in the variables you know	mass = 0.754 g/cm3 x 9.62 cm3
Step 3	Calculate mass by combining terms (don't forget units)	mass = 7.25 grams

Now that we have the mass of a rocket fin made from card stock #2, let's calculate the mass of a fin made from foam board. The density of the foam board is 0.125 g/cm³. The foam board is thicker than the card stock but we will keep the width and length the same. The foam board rocket fin has a size of 0.635 cm x 5.08 cm x 10.16 cm. Again we must first calculate volume:

Step 1	Write out equation for volume	volume = thickness x width x length
Step 2	Fill in the variables you know	volume = 0.635 cm x 5.08 cm x 10.16 cm
Step 3	Calculate volume by combining terms (don't forget units)	volume = 32.77 cm3

Next we would calculate the mass:

Step 1	Write out equation for mass	mass = density x volume
Step 2	Fill in the variables you know	mass = 0.125 g/cm3 x 32.77 cm3
Step 3	Calculate mass by combining terms (don't forget units)	mass = 4.096 grams

Even with the extra volume of the foam board fin due to the thickness, the mass of the foam board fin is much less as a result of the lower density. Knowing that mass is proportional to weight we should choose the material with the lowest mass and calculate weight. Using the mass of the foam board fin we will calculate its weight:

Step 1	We need to convert the mass in grams to kilograms	mass = 4.096 g x 0.001 mass = 0.004096 kg
Step 2	Write of the equation for weight	weight = mass x gravity
Step 3	Fill in the variables you know	weight = 0.004096 kg x 9.8 m/s2
Step 4	Calculate weight by combining terms (don't forget units)	weight = 0.0401 kgm/s2 or 0.0401 Newtons