Mission Definition Review: SR-1

Document Ref: OMSA-SR-1-MDR
Program: Early Sounding Rockets
Vehicle: Skybreaker I
Target Launch: February 1951

STATUS: MISSION APPROVED

1. Mission Overview

1.1 Strategic Context

SR-1 "First Spark" is the first launch of the new agency, laying the foundations for the Early Sounding Rockets campaign - and aiming to complete the first contract in the Early Sounding Rockets program.
It will be the first test of the Skybreaker I vehicle and, if the launch is successful, will gather initial pressure/temperature data from the lower atmosphere and validate our aerodynamic models for future high-altitude Kármán line attempts.

This mission aims to complete the contract for "First Flight".

1.2 Mission Objectives

Objectives are tiered to allow for partial mission success analysis.

Serial	Objective	Source
1	Reach the desired altitude and climb rate requirements.	Contract
2	Validate the sounding rocket performance model for use in future missions.	OMSA Engineering
2	Gather low atmosphere Earth science and test the instruments	OMSA Science

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2. Requirements & Constraints

2.1 Trajectory and Attitude Control

Serial	Requirement	Type	Source
1.1	The vehicle must reach a maximum altitude of at least 1000 m.	Threshold	Contract
1.2	The vehicle should reach a maximum altitude of at least 15,000 m.	Goal	OMSA Engineering
1.3	The vehicle should reach a maximum rate of climb of at least 50 m/s.	Threshold	Contract
1.4	The trajectory must only take the vehicle over unpopulated areas.	Threshold	Range Safety

2.2 Payload & Science

Serial	Requirement	Type	Source
2.1	Temperature measurements should be made in-flight in the low atmosphere.	Goal	OMSA Science
2.2	Barometer measurements should be made in-flight in the low atmosphere.	Goal	OMSA Science
2.3	The payload should transmit scientific data back to the ground while in flight.	Goal	OMSA Science

2.3 Power & Avionics

Serial	Requirement	Type	Source
3.1	Battery capacity must be sufficient for the entire mission.	Threshold	OMSA Engineering
3.2	Avionics must be sufficient to allow reading of payload instrument data and basic telemetry	Threshold	OMSA Engineering

3 Preliminary Analysis

The preliminary analysis will be used as a basis for the design of the 'Skybreaker I' vehicle and will cover the following:

• Delta-V Requirements
• Flight Time Estimate
• Power Budget

In this analysis we make the following assumptions:

3.1 Delta-V Requirements

To estimate the required performance, we equate the kinetic energy at burnout to the potential energy at apogee, accounting for losses during the powered ascent.

$$mgh = \frac{1}{2} mv^2$$

combined with:

$$v = \Delta V_{usable} = \Delta V_{propellant} - gt_{burn} - (1-k_{drag})\Delta V_{propellant}$$

results in:

$$\Delta V_{propellant} = \cfrac{\sqrt{2gh} + gt_{burn}}{1-k_{drag}}$$

where $h$ is the altitude above ground level, $t_{burn}$ is the engine burn time, $k_{drag}$ is the proportion of the propellant's delta-v that is 'lost' to drag, and $g$ is the gravitational constant.

When the propellant Delta-V required is plotted against the target height, with a $t_{burn}$ of 50s (assuming an early generation Aerobee engine) the following graph is produced.

Assuming $k_{drag}$ is 0.2, the Delta-V required is estimated to be $1291 m/s$

3.2 Flight Time Estimate

The flight time is required in order to size the power subsystem and will be estimated by combining the burn time, coast time, and fall time, assuming drag is negligible.

$$T = t_{burn} + t_{coast} + t_{fall}$$

where $t_{coast} = k_{coast}t_{burn}$ (an empirical assumption) and $t_{fall} = \sqrt{\cfrac{2h}{g}}$ (from SUVAT).

If $t_{burn} = 50$, $k_{coast} = 0.4$, and $h = 15000$ then $T = 125.3$ seconds.

3.3 Power Budget

If the above flight time is taken, with a safety factor of 2, and an initial assumption of a power consumption of 100 W, the required energy storage is:

$$125.3 * 2 * 0.1 = 25.1 kJ$$

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3. Concept of Operations

The mission profile consists of five distinct phases:

• Phase 0: Pre-Launch - Confirm all systems are functioning correctly.

• Phase I: Launch - Engine ignition, clamp release, and spin-stabilization.

• Phase II: Unpowered Ascent (Coast) - Immediately following burnout (~T+50s) the vehicle coasts to apogee.

• Phase III: Apogee - Maximum altitude is reached.

• Phase IV: Descent - Unpowered and uncontrolled descent.

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4. Risk Register

Serial	Risk	Mitigatation	Severity
1	Uncontrolled catastrophic failure (explosion)	All personnel to be clear of pad.	High
2	Engine failure	Engines are static tested prior to flight.	Medium
3	Debris striking personnel or structres	Vehicle to be launched at a small angle towards the sea. Range safety device to be installed if possible.	Medium