![]() ![]() Note: do not plug negative 9.81 into the equation, the minus sign is already accounted for. g is acceleration due to gravity, which is 9.81 meters per second squared (m/s 2).m avg is the rocket's average mass in kilograms (kg).T avg is the engine's average thrust in newtons (N).a boost is the rocket's acceleration during the boost phase in meters per second squared (m/s 2).The average acceleration during the boost phase can be calculated using Newton's second law (see technical note): Equation 3: To solve for the maximum height in this equation, first you need to find the boost phase acceleration, a boost, and the maximum velocity, v max. Note: Do not plug negative 9.81 into the equation, the minus sign is already accounted for. v max is the rocket's maximum velocity, which is achieved at the end of the boost phase, in meters per second (m/s).a boost is the rocket's acceleration during the boost phase, in meters per second squared (m/s 2).h max is the rocket's maximum height, in meters (m).This height is the sum of the height the rocket reaches at the end of its boost phase plus the additional height it gains during the coast phase. This means that you can roughly predict a rocket's maximum height using a simplified equation that assumes the rocket's mass is constant. Less than 10% of the rocket's weight at launch is propellant. For example, the model rocket at the bottom of Figure 1 (the Apogee Apprentice) has a mass of 60.8 g when loaded with a new A8-3 model rocket engine, and a mass of 54.9 g with a used engine (we will discuss model rocket engines and what the letters and numbers mean below), a difference of 5.9 g. However, the propellant mass fraction is much lower for model rockets. Reaching orbit requires so much fuel that the majority-nearly or sometimes exceeding 90%-of a rocket's mass at launch is fuel (this ratio is called the propellant mass fraction). This equation is extremely important for real rockets that fly into space. As the engine burns and expels fuel, its mass decreases therefore, rocket motion is modeled mathematically with the Tsiolkovsky rocket equation (see Bibliography), which takes the rocket's changing mass into account. However, that presents a problem when applied to rockets: their mass is not constant! Rockets expel high-velocity exhaust in one direction, which pushes the rocket in the other direction due to conservation of momentum. In high school physics problems, Newton's second law is usually applied to objects with constant mass (for instance, the classic example of a force pushing a block on an inclined plane). a is acceleration, in meters per second squared (m/s 2).We have briefly covered how you can measure rocket flight, but how can you predict a rocket's motion? You are probably familiar with Newton's second law of motion, which is commonly expressed in equation form as: Equation 1: The Jolly Logic Altimeter Three software showing recorded flight data. ![]()
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