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Article |
Fundamentos Físicos y Matemáticos de la Seguridad
Operacional Aeroportuaria: Aeropuerto Internacional Cotopaxi-Ecuador
Jorge Milton Lara-Sinaluisa[*]
Juan Manuel Martínez-Nogales*
Jéssica Moreno-Ayala*
Abstract
This article presents a technical and scientific
analysis of the application of physical and mathematical principles in the
design of a risk management model for Cotopaxi International Airport in
Ecuador. The research is based on international standards established by the
International Civil Aviation Organization (ICAO). It employed quantitative and
qualitative analysis through technical observation of airport infrastructure,
probabilistic assessment of operational risks, analysis of atmospheric physical
variables, and the application of mathematical matrices— , severity, and
probability. From a physical standpoint, it was determined that factors such as
altitude, atmospheric density, material strength, and coefficients of friction
directly affect landing and takeoff operations. Mathematical risk assessment models
made it possible to establish critical levels of operational tolerability. It
is concluded that the implementation of an Operational Safety Management System
(SMS) based on physical and mathematical principles significantly improves the
predictive and preventive capabilities regarding airport incidents. The study
demonstrates that the integration of quantitative analysis into airport
management increases operational efficiency, minimizes risks, and strengthens
the sustainability of air transport.
Keywords: operational safety, aeronautical physics, mathematical
analysis, risk management, civil aviation.
Resumen
El artículo desarrolla un
análisis técnico-científico de aplicación de fundamentos físicos y matemáticos
en el diseño de un modelo de gestión de riesgos para el Aeropuerto
Internacional Cotopaxi, Ecuador. La investigación se fundamenta en los
estándares internacionales establecidos por la Organización de Aviación Civil
Internacional (OACI). Empleó análisis cuantitativo y cualitativo mediante
observación técnica de infraestructura aeroportuaria, evaluación probabilística
de riesgos operacionales, análisis de variables físicas atmosféricas y
aplicación de matrices matemáticas de severidad y probabilidad. Desde el punto
de vista físico, se identificó que factores como altitud, densidad atmosférica,
resistencia de materiales y coeficientes de fricción afectan directamente las
operaciones de aterrizaje y despegue. Los modelos matemáticos de evaluación de
riesgos permitieron establecer niveles críticos de tolerabilidad operacional.
Se concluye que la implementación de un Sistema de Gestión de Seguridad
Operacional (SMS) basado en principios físicos y matemáticos mejora significativamente
la capacidad predictiva y preventiva de incidentes aeroportuarios. El estudio
demuestra que la integración de análisis cuantitativos en la gestión
aeroportuaria incrementa la eficiencia operativa, minimiza riesgos y fortalece
la sostenibilidad del transporte aéreo.
Palabras clave: seguridad operacional, física aeronáutica, análisis matemático, gestión
de riesgos, aviación civil.
Introduction
Civil aviation represents one of the most complex and
multifaceted technological infrastructures ever designed by humans, primarily
due to the intricate and simultaneous interaction of a myriad of factors
encompassing physical elements, mathematical formulations, human behavior, and
environmental considerations that collectively influence operational
effectiveness. Within this intricate framework, airport operational safety
emerges as an essential aspect that depends fundamentally on the precise and
accurate application of established scientific principles related to classical
mechanics, aerodynamics, strength of materials, fluid dynamics, probabilistic
statistical analysis, and the theoretical foundations of risk management (Liu, 2026;
Stroeve et al., 2016) .
Cotopaxi International
Airport, located in the city of Latacunga in Ecuador’s central highlands, is of
strategic importance to national air transport due to its geographic location
and operational capacity. However, the gradual increase in military and private
air operations has placed new technical demands on the airport infrastructure
and operational safety management systems.
From a comprehensive physical
perspective, the operational capabilities of airports are significantly
influenced and determined by a variety of fundamental variables, including,
among others, atmospheric pressure, air density, ambient temperature, wind speed,
the coefficient of friction between the runway and aircraft tires, as well as
the structural integrity and strength of the pavement surfaces. The elevation
of Cotopaxi International Airport, located at an impressive altitude of
approximately 2,800 meters above sea level, introduces a unique set of
meteorological conditions that ultimately alter the aerodynamic characteristics
of various aircraft, affecting crucial operational parameters such as the
required takeoff distance, the distance required for effective braking, and the
overall performance of aircraft engines in real-world scenarios (Saputra & Soehodho, 2025; Sivakumar, 2022) .
The contemporary operational
safety paradigm has undergone a significant transformation, shifting away from
historically reactive methodologies that primarily address incidents after they
occur, toward sophisticated predictive frameworks that are meticulously
grounded in mathematical probability theories and comprehensive severity
assessments. The Safety Management Systems (SMS) that the International Civil
Aviation Organization (ICAO) has meticulously formulated and established serve
to effectively integrate advanced quantitative models that are essential for
the precise identification, comprehensive assessment, and strategic mitigation
of the various aviation risks that may arise in the aviation sector. These
sophisticated systems employ a wide range of statistical tools, intricate
probabilistic matrices, and multi-criteria decision-making models that work in
concert to accurately estimate and determine what constitutes acceptable levels
of risk in the context of aviation operations. Therefore, the evolution of
these methodologies represents a fundamental advance in the field of
operational safety, as it reflects a deep understanding of risk management that
is both proactive and based on empirical anddata .
The integration of artificial
intelligence and advanced decision-making frameworks into airport management
has significantly revolutionized methodologies for forecasting and mitigating
operational risks. Contemporary studies indicate that the application of
machine learning techniques, multi-criteria evaluation, and intelligent
networks facilitates the improvement of aviation systems’ resilience in a
context of considerable operational unpredictability. AlMarri, Bahroun, and Hassan (2026) highlight
that artificial intelligence applied to airport transportation improves
predictive capabilities regarding operational, environmental, and security
threats through automated models capable of analyzing large volumes of data in
real time. Complementing this approach, Yang (2026)
demonstrates that multifactorial predictive models based on machine
learning enable the identification of risk patterns during ongoing airport
operations, reducing disruptions and enhancing operational efficiency.
Similarly, Jahangoshai Rezaee and Yousefi (2018) propose
intelligent multi-criteria analysis systems that integrate probabilistic,
operational, and human variables to prioritize airport threats and optimize
strategic decision-making. Meanwhile, Li et al. (2016)
incorporate quantitative mathematical models and complex network theory to
assess the vulnerability of aviation systems to localized threats, enabling the
design of resilience strategies capable of minimizing operational disruptions
and ensuring the continuity of air transport. Taken together, these studies
demonstrate that the integration of artificial intelligence, mathematical
modeling, and multi-criteria analysis constitutes a fundamental tool for the
development of smart, resilient, and sustainable airports.
In mathematical terms, airport
risk management can be expressed through probabilistic models of adverse event
occurrence. The quantitative assessment of operational risk is given by the
following relationship:
Where:
R = Risk
P = Probability
S =
Severity
This model forms the mathematical basis for modern
operational safety systems implemented in the aviation industry.
The objective of this study
was to conduct a scientific analysis of airport operational safety by
integrating physical and mathematical principles applied to Cotopaxi
International Airport. The study aimed to demonstrate that the rigorous
application of scientific principles allows for the optimization of airport
management, the minimization of operational risks, and the strengthening of air
transport sustainability.
The scientific significance of
this research lies in the interdisciplinary integration of applied physics,
aeronautical engineering, mathematical analysis, and operational management.
Similarly, the study provides a quantitative perspective that enhances
traditional airport evaluation models.
Operational
Safety in Civil Aviation
Aviation operational safety is characterized by the condition in which
hazards related to air operations are mitigated and controlled to acceptable
thresholds through a continuous process of hazard identification and risk
assessment (Heidt et al., 2016; Rey et al.,
2021; Yu et al., 2025) .
The International Civil Aviation Organization (ICAO), through Annex 19,
requires that each airport establish an operational safety management system
(SMS) capable of integrating technical, administrative, and operational
protocols designed to reduce incidents and accidents.
From a systemic perspective,
operational safety encompasses:
· Human factors
· Physical elements.
· Meteorological variables.
· Airport infrastructure.
· Technological frameworks.
· Mathematical management models.
The
interaction between these elements determines the operational stability of the
airport system.
Physical Fundamentals Applied to Airport Operations
Aerodynamics and Atmospheric Conditions
Takeoff and landing operations
depend directly on aerodynamic principles associated with lift and drag (Bueso & Betancourt, 2017; Skorupski, 2016) .
Lift is
expressed by:
·
Where:
·
L = lift.
·
V = relative velocity.
·
S = wing area.
·
Atmospheric density decreases
significantly with altitude, affecting the ability to generate lift. Because
Cotopaxi International Airport is located in a high-altitude Andean region,
aircraft require longer takeoff and landing distances.
Airport runways are subjected to
dynamic loads generated by heavy aircraft. The structural strength of the
pavement depends on physical properties such as the modulus of elasticity,
compressive strength, and fatigue resistance of materials (Claros et al.,
2017; Wang et al., 2026) .
The
mechanical stress applied to the pavement can be expressed as:
Where:
· F = applied force.
· A = contact area.
Cracks identified on the airport’s
operational apron represent stress concentrators that increase the probability
of structural failure.
Safety during landing depends on
the coefficient of friction between the tires and the runway.
The minimum
braking distance is given by:
Where:
· d = braking distance.
· V = landing speed.
· g = gravitational acceleration.
The presence of moisture, cracks,
or surface deterioration reduces the coefficient of friction and increases the
risk of runway excursions.
Mathematical Models for Risk
Management
Aviation risk management uses
probabilistic models to estimate occurrence and scenarios .
The
cumulative probability of failure can be modeled using Poisson distributions:
Where:
P(X=k) = Probability that k
events will occur
λ = Expected average number of occurrences
e = Euler’s constant
k! = Factorial of k
In turn, multi-criteria assessment
uses severity and probability matrices to classify operational risks
(Sivakumar, 2022; Yu et al., 2025) .
Airport risks can be classified according to:
|
Probability |
Low
Severity |
Medium Severity |
High
Severity |
|
Low |
Acceptable risk |
Moderate risk |
Significant risk |
|
Average |
Moderate risk |
High risk |
Critical risk |
|
High |
High risk |
Critical risk |
Unacceptable risk |
This approach allows for the
prioritization of technical interventions and the optimization of operational
resources.
Applicable International
Regulations
ICAO Annex 14 establishes
specifications related to:
· Runway geometric design.
· Airport signage.
· Lighting systems.
· Safety strips.
· RESA areas.
· Taxiways.
· Airport obstacles.
For its part, Annex 19 regulates
Operational Safety Management Systems (SMS), promoting preventive and
predictive models.
Materials and methods
The research was conducted using a mixed-methods
approach with a quantitative focus, integrating physical-mathematical analyses
and a qualitative assessment of operational conditions.
The study adopted a non-experimental design of a
descriptive, correlational, and applied nature. The
methodology was structured into four fundamental phases:
· Technical diagnosis of infrastructure.
· Physical and operational assessment.
· Mathematical risk modeling.
· Design of mitigation strategies.
A census
sampling method was used due to the small size of the population.
· Data Collection Techniques and Instruments
· The techniques used were:
· Direct technical observation.
· Structured surveys.
· Semi-structured interviews.
· Airport inspection forms.
· Document analysis.
The instruments used included:
· Likert-type questionnaires.
· Observation guides.
· Risk assessment matrices.
· Operational frequency statistical models.
· The quantitative analysis included:
· Descriptive statistics.
· Probabilistic analysis.
· Multi-criteria matrices.
· Severity assessment.
· Calculation of risk indices.
The overall
operational index was estimated using the following formula:
Where:
IOR =
Operational Risk Index.
The physical-operational study considered:
Effective runway length.
Pavement conditions.
Coefficient of friction.
Atmospheric density.
Ambient temperature.
Slope gradients.
Operational lighting.
Structural strength.
Critical meteorological factors such as crosswind, relative humidity, and
horizontal visibility were also evaluated.
Based on
the criteria of Rios Insua et al. (2018) , methodological reliability was validated through:
· Triangulation of information.
· ICAO regulatory comparison.
· Statistical consistency analysis.
· Technical verification of observations.
Results
The technical analysis revealed significant
deterioration in various operational areas of the airport.
The
following were identified:
· Longitudinal cracks.
· Surface wear.
· Reduced coefficient of friction.
Presence of
structural deformations.
From a
physical standpoint, surface irregularities disrupt the uniform distribution of
loads and increase the risk of hydroplaning.
The
observed operational coefficient of friction was below the values recommended
by ICAO under wet conditions.
Atmospheric
and Aerodynamic Assessment
The airport’s altitude results in reduced atmospheric density, affecting:
· Engine performance.
· Aerodynamic lift.
· Takeoff run distance.
· Braking capacity.
Atmospheric density can be approximated using:
Where:
P = atmospheric pressure.
R = specific constant of air.
T = absolute temperature.
A decrease in density reduces the aerodynamic efficiency of aircraft.
Statistical analysis identified the following major risks:
|
Risk |
Probability |
Severity |
Level |
|
Runway Excursion |
High |
High |
Critical |
|
Unauthorized entry |
Medium |
High |
High |
|
Lighting failure |
Medium |
Medium |
Moderate |
|
Ground collision |
Low |
High |
Moderate |
|
Structural pavement failure |
High |
Medium |
High |
The results show a predominance of risks related to infrastructure and
perimeter control.
The results indicated:
·
78% of staff
consider current operational security measures to be insufficient.
·
82% recognize
the need for ongoing technical training.
·
69% identify
critical deterioration in infrastructure.
·
91% believe it
is necessary to implement a comprehensive SMS.
Physical Assessment of Lighting and Signage
Inconsistencies were detected in:
· Light intensity.
· Sign reflectivity.
· Lighting uniformity.
· Markings on traffic lanes.
From a physical perspective, reduced light intensity affects nighttime
visual perception and slows drivers’ reaction times.
Predictive Risk Modeling
The probabilistic simulation showed that
implementing corrective measures can reduce potentially hazardous events by up
to 63%.
The predictive model revealed a positive correlation
between:
· Structural condition of pavements.
· Coefficient of friction.
· Probability of lane departure.
The results obtained demonstrate that airport
operational safety cannot be limited solely to administrative procedures but
must be based on quantifiable scientific principles.
From a physical standpoint, the altitude of Cotopaxi
International Airport represents a critical variable that significantly affects
aircraft performance. Reduced atmospheric density decreases lift and
necessitates higher operating speeds, thereby increasing the structural demands
on the runway. The deterioration observed in the pavement increases localized
stresses and reduces the capacity to dissipate dynamic loads. This phenomenon
is consistent with international research on structural fatigue at
high-altitude airfields.
Mathematically, the probabilistic models used
demonstrated a high predictive capacity for identifying critical operational
scenarios. The use of risk matrices made it possible to prioritize
vulnerabilities and optimize mitigation strategies.
The research shows that modern airport systems must
incorporate quantitative analysis tools capable of integrating physical, human,
and operational variables. The findings are consistent with previous research
conducted at airports in Ecuador, Honduras, and Colombia, where the
implementation of SMS systems based on technical analysis significantly reduced
the occurrence of incidents.
Furthermore, the research confirms that airport
infrastructure constitutes a dynamic system continuously subjected to variable
physical loads. Therefore, operational safety management must include
continuous monitoring using mathematical models of structural behavior.
The study also highlights the importance of the
human factor. The lack of specialized technical training increases the
likelihood of operational errors. Based on human reliability theory, human
errors can be modeled probabilistically and reduced through continuous
training.
Finally, the research demonstrates that
interdisciplinary integration among physics, mathematics, and aeronautical
engineering significantly strengthens airport management models.
Implementation of an Integrated SMS System
We propose implementing an Operational Safety Management System
consisting of:
· Continuous structural monitoring.
· Probabilistic risk assessment.
· Digital tracking systems.
· Specialized technical training.
· Periodic physical inspection.
Physical
Rehabilitation of Pavements
Priority actions include:
· Repair of structural cracks.
· Improvement of drainage systems.
·
Increasing the
coefficient of friction.
· Reinforcing road surfaces.
Recommended:
·
Replacement of
damaged light fixtures.
· Implementation of LED lighting.
· Photometric calibration.
· Increase reflectivity.
Strengthening
Perimeter Security
Proposed:
· Renovation of perimeter fences.
· Smart sensors.
· Video surveillance.
· Automated access control.
Integration of predictive mathematical models
· Operational management must incorporate:
· Predictive algorithms.
· Continuous statistical analysis.
· Operational simulation.
· Dynamic risk assessment.
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Master's Degree in Physics. Faculty Member and
Researcher, Transportation Management Program, Chimborazo Higher Polytechnic
School (ESPOCH)
https://orcid.org/0000-0002-3116-5161
Master’s Degree in Physics. Research Professor,
Automotive Engineering Program, Chimborazo Higher Polytechnic School (ESPOCH)
https://orcid.org/0000-0002-4860-1548
Master’s Degree in
Aeronautical Systems Management. Research Professor, Transportation Management
Program, Chimborazo Higher Polytechnic School (ESPOCH)
https://orcid.org/0000-0003-0085-9459