Skip to main content

Roots

To those who carry the lineage of coil and curl, of wave and kink, we speak to you, recognizing the vibrant story held within each strand. Your hair, a living testament to journeys through time, to ancestral strength, often yearns for a particular kind of guardianship. It is a care passed down through generations, shaped by the sun-drenched lands of Africa, the resilient spirit of the diaspora, and the whispered wisdom of foremothers.

This exploration delves into the practice of oil application, not merely as a modern beauty step, but as a continuation of deeply rooted traditions. We unravel how this ancient art safeguards textured hair from the everyday tolls, echoing a heritage of protection and beauty.

The monochrome portrait celebrates the beauty of braided textured hair, echoing ancestral strength and cultural expression. The meticulous braiding technique highlights the diverse styling possibilities within Black hair traditions, while the subject's gaze embodies resilience and a deep connection to heritage through thoughtful expressive styling choices and holistic hair care philosophies.

What is the Foundational Structure of Textured Hair?

The intrinsic architecture of textured hair, characterized by its elliptical cross-section and helical growth pattern, influences how it interacts with moisture and external elements. Unlike straighter hair types, the winding path of a textured strand creates numerous points where the cuticle, the hair’s outermost protective layer, is raised or exposed. This structural characteristic, while lending itself to incredible volume and visual depth, also means natural sebum, the scalp’s own conditioning oil, struggles to travel down the entire length of the hair fiber. This leads to inherent dryness and increased susceptibility to damage from environmental stressors or styling.

Understanding the very makeup of these fibers is key. Hair is composed primarily of keratin proteins. Within these keratin structures, lipids play a significant part in maintaining the hair’s integrity, offering a barrier against external factors. These lipids, a blend of fatty acids, ceramides, and cholesterols, exist both within the hair shaft and as a coating from sebaceous glands on the surface.

Afro-textured hair, specifically, exhibits a higher overall lipid content, particularly apolar lipids, compared to European or Asian hair, which influences its interaction with water and its radial swelling. Despite this internal lipid richness, the unique helical shape means these lipids are not as evenly distributed along the hair shaft, contributing to its common dryness.

The intrinsic helical pattern of textured hair inherently limits sebum distribution, making oil application a vital supplemental guard against daily wear.

Hands extract aloe vera pulp for a traditional hair treatment, connecting generations through natural haircare rituals. This image represents a tangible link to ancestral heritage and the enduring beauty of holistic textured hair care practices promoting optimal scalp health and resilient hair formations.

How does Oil Application Align with Hair’s Elemental Biology?

The application of external oils mimics and supplements the hair’s natural lipid layer. When oils are applied to textured hair, they interact with the cuticle, settling into the spaces between the lifted scales. This action helps to smooth the cuticle, creating a more uniform surface. A smoother cuticle means less friction between strands, which reduces tangling and, in turn, minimizes physical breakage during manipulation—a common occurrence for hair with many curves and turns.

Beyond surface smoothing, certain oils possess the ability to penetrate the hair shaft itself, moving past the cuticle and into the cortex. This deep penetration is particularly important for moisturizing the inner structure of the hair, making it more pliable and less prone to brittleness. Coconut oil, for instance, has a molecular structure that allows it to penetrate the hair fiber, reducing protein loss both before and after washing. This property speaks to a deeper interaction than merely coating the surface.

By replenishing lipids, oils help to reinforce the hair’s natural barrier function, improving its elasticity and its capacity to resist stress. This scientific understanding, now articulated through modern research, echoes the generations of oral tradition and observation that informed ancestral care practices.

The ancestral knowledge of plant-based remedies for hair is well-documented across various indigenous communities globally. In Africa, for example, the Himba tribe in Namibia uses a mixture of red ochre paste called otjize, which includes butterfat, to protect their hair from sun and insects. Similarly, traditional practices in Ethiopian communities incorporate various plants for hair and skin care, with leaves often used as treatments or cleansing agents. This demonstrates a long-standing understanding that external applications from nature protect and sustain hair in challenging environments.

Region or Culture Ancient Egypt
Traditional Oil/Fat Application Various plant oils (castor, sesame, moringa, olive)
Protective Mechanism (Ancestral Understanding) Nourishment, shine, protection from sun and dryness. Cleopatra was known for anointing her body with oils.
Region or Culture African Tribes (e.g. Himba, Basara)
Traditional Oil/Fat Application Shea butter, Chebe powder (mixed with oils/fats), otjize (butterfat & ochre)
Protective Mechanism (Ancestral Understanding) Moisturizing, length retention, protection from harsh environmental conditions, sun, and insects.
Region or Culture Indigenous Australians
Traditional Oil/Fat Application Emu oil, kangaroo fat, eucalyptus, Melaleuca quinquenervia (tea tree) oil
Protective Mechanism (Ancestral Understanding) Deep conditioning, insect repellent, antimicrobial properties, protection against elements.
Region or Culture Caribbean Communities
Traditional Oil/Fat Application Castor oil (often mixed with olive or coconut), aloe vera
Protective Mechanism (Ancestral Understanding) Scalp nourishment, hair growth, moisture, cooling, protection.
Region or Culture These practices illuminate a shared ancestral understanding of oils as guardians for hair against diverse environmental aggressors.

Ritual

The application of oils to textured hair stands as a ritual, a careful practice refined through centuries. It is an art form, a dance between human hands and the hair’s natural inclination, a tradition passed down with reverence. The method transcends mere product use; it encompasses the rhythmic sectioning of hair, the mindful working of oil from root to tip, and the often-shared moments that accompany these acts. For communities of Black and mixed-race descent, this ritual connects to a lineage of resilience, where hair care was not just about aesthetics but about preserving identity and resisting erasure.

The image conveys a moment of intimate care, as hands apply a rich moisturizer to tightly coiled hair, celebrating the beauty and strength of Black hair traditions and holistic care. This act embodies cultural identity, ancestral connection, and wellness for expressive styling, nourishing the hair's natural resilience.

How Have Ancestral Styling Traditions Preserved Hair through Oil?

Many traditional styling practices for textured hair are inherently protective. Styles like braids, twists, and cornrows, which trace their ancestry back thousands of years in Africa, reduce the hair’s exposure to manipulation and environmental elements. Within these styles, oil application plays a significant role.

Before the hair is gathered into these intricate formations, oils are often applied to coat the individual strands, creating a slippery surface that minimizes friction during the braiding or twisting process. This lubrication helps to prevent breakage, a common concern for the delicate coils of textured hair.

The Basara tribe of T’Chad, renowned for their incredible hair length, uses an herb-infused oil and animal fat mixture, often called Chebe, applied weekly before braiding their hair. This historical practice illustrates a direct correlation between oil application, protective styling, and length retention, a goal central to hair health across generations. The oil allows the hair to remain supple within its protective confines, delaying dryness and brittleness. When hair is tucked away in braids or twists, the oil creates a barrier against dust, dry air, and harsh sunlight, elements that can strip moisture and cause damage.

Oil application, when integrated into traditional protective styling, becomes an ancestral shield, buffering textured strands against the wear of daily existence.

Embracing self-expression, the subject's strong undercut and focused gaze reflect contemporary beauty, echoing themes of personal freedom within textured hair narratives. This image blends modern styling with timeless elegance, embodying holistic hair care practices, enhanced by dramatic lighting.

What Role does Oil Play in Enhancing Hair Definition?

Beyond protection within styles, oils also contribute to the aesthetic integrity of textured hair, particularly in defining curl patterns. For hair that naturally forms coils and waves, moisture is paramount for vibrant definition. Oils, while not moisturizers themselves, act as occlusives, sealing in the water that the hair has absorbed.

This sealing action helps to maintain the hydrated state of the hair, allowing individual curls to clump together and hold their shape with more integrity. When applied to damp hair, a light layer of oil can encourage the natural curl pattern to become more pronounced, reducing frizz and promoting a polished finish.

Consider the meticulous ritual of finger coiling or shingling, techniques that sculpt individual curl groupings. A touch of oil on the fingertips during these processes can aid in distributing the product evenly, ensuring each coil receives its share of protective coating. This technique creates a smooth, reflective surface on the hair, giving it a healthy sheen.

The presence of fatty acids and antioxidants in many natural oils, such as argan or olive oil, further contributes to this visible vitality, safeguarding the hair from environmental factors like UV rays. The luminosity imparted by careful oil application speaks to a desire for beauty that transcends time, a beauty celebrated and preserved through mindful care.

The evolution of hair care tools, from the wide-toothed combs crafted from natural materials in ancient Africa to the specialized implements of today, also speaks to the consistent need for gentle manipulation alongside oil application.

  1. Wooden Combs ❉ Historically carved from wood or bone, these tools were used to detangle hair after oiling, minimizing breakage. Their wide teeth glided through oiled strands.
  2. Fingers ❉ Often the primary tool, hands were used to distribute oils and work them through the hair, creating intimate moments of care. This allowed for sensory connection and precise application.
  3. Head Wraps ❉ After oiling and styling, head wraps (gele, duku, ghoema, etc.) served not only as adornment but also as a protective layer, preserving the style and preventing moisture loss from the oiled hair.

Relay

The relay of knowledge, from elder to youth, from ancestor to descendant, breathes life into the care of textured hair. This is not merely about instructions; it is about the living memory of touch, the subtle rhythms of practice, and the unwavering belief in the hair’s inherent sacredness. The journey of oil application, from elemental protection to a personal ritual, ultimately culminates in a holistic approach to hair wellness, drawing upon ancestral wisdom to solve contemporary challenges. It is a story of continuity, where modern science often illuminates the ‘why’ behind practices long held sacred.

A tender gesture of ancestral hair care traditions, captured in monochrome, showcases the application of natural ingredients, symbolizing heritage and wellness. This image honors cultural practices while nurturing tightly coiled textures, fostering self-love and communal connection with time-honored Black hair traditions.

How does Oil Application Support Holistic Hair Wellness through Ancestral Wisdom?

The concept of holistic wellness, deeply woven into many ancestral cultures, recognized that the health of the hair was connected to the health of the whole person. This comprehensive view often influenced traditional hair care regimens. The practice of oiling the scalp, a ritual common across African and South Asian traditions, was not only for the hair itself but also for invigorating the scalp, promoting blood flow, and creating a balanced environment for growth. This connection between scalp health and hair vitality is a timeless truth that modern understanding affirms.

For generations, particularly within Black communities, the act of applying oil or “greasing” the scalp was a foundational aspect of care, a cherished memory often tied to a grandmother’s or mother’s gentle hands. While some modern perspectives caution against excessive scalp oiling due to potential pore clogging, the underlying intention was always nourishment and protection. Many traditional applications were likely more sparse or used different formulations, or even applied to the hair itself rather than saturating the scalp with thick petroleum-based greases that came later. The original wisdom centered on providing a beneficial lipid barrier.

The age-old gesture of oiling textured hair, often an intimate moment of familial care, quietly speaks to a science of protection, ensuring the vitality of strands and honoring a shared past.

A powerful instance of this ancestral wisdom validating modern scientific insight comes from the widespread use of oils like coconut oil. Research has shown that coconut oil can reduce protein loss in hair. This scientific finding provides empirical backing to a practice that has existed for centuries in many cultures, including those with textured hair traditions, where coconut oil has been a staple for nourishing and protecting strands. This consistency across time and cultures highlights a profound, inherited understanding of how natural elements interact with hair structure.

The wisdom of traditional hair care, where oiling was an integral component, can be seen in its capacity to address common hair challenges, transforming them from problems into opportunities for mindful care.

  • Dryness ❉ Textured hair’s helical shape means sebum often struggles to travel down the strand. Oils seal in moisture, a practice evident in West African traditions where oils and butters kept hair hydrated in dry climates.
  • Breakage ❉ By lubricating the hair cuticle and sometimes penetrating the cortex, oils reduce friction and reinforce the hair’s structure, minimizing breakage from manipulation or environmental stressors. This aligns with protective styling history.
  • Environmental Damage ❉ Oils form a protective layer against sun exposure, wind, and pollution. The Himba tribe’s use of butterfat and ochre to guard against the sun is a historical testament to this.
The application of clay to textured hair braids evokes ancestral traditions, symbolizing a connection to heritage and holistic hair wellness practices. This intimate moment emphasizes the care invested in maintaining strong, culturally significant hair formations and scalp health with natural ingredients.

How do Nighttime Rituals Safeguard Hair Using Oil?

Nighttime offers a unique opportunity for concentrated hair care, a practice deeply ingrained in the wisdom of our ancestors who understood the importance of protecting hair during rest. The simple ritual of covering hair with a bonnet or scarf, often after a light application of oil, serves as a profound act of preservation. This practice shields hair from friction against rough pillowcases, which can lead to breakage, split ends, and tangling for delicate textured strands.

The modern bonnet, whether silk or satin, descends from head coverings used by women of the diaspora for both practical and symbolic purposes. These coverings helped maintain intricate hairstyles for days or weeks, a necessity when daily washing was not feasible or desired. The underlying principle was protection.

Applying a modest amount of oil—perhaps a nourishing blend of jojoba and argan, which resemble natural sebum and provide antioxidants—before donning a bonnet helps to seal in moisture from the day’s conditioning treatments. This creates a closed, humid environment that allows the hair to remain supple and less prone to moisture loss overnight.

Consider the impact on the hair’s lipid content and overall health. While African hair naturally possesses a high lipid content, it is also prone to rapid moisture loss due to its unique structure. The external application of oils, particularly before protective wrapping, supplements these natural lipids and acts as an additional barrier against dehydration.

This strategic nightly care prevents the exacerbation of dryness that makes textured hair more susceptible to breakage, a cyclical challenge that generations have sought to address. The consistency of this ritual across countless households speaks to its proven effectiveness, a quiet testament to inherited knowledge.

Relay

The relay of knowledge, from elder to youth, from ancestor to descendant, breathes life into the care of textured hair. This is not merely about instructions; it is about the living memory of touch, the subtle rhythms of practice, and the unwavering belief in the hair’s inherent sacredness. The journey of oil application, from elemental protection to a personal ritual, ultimately culminates in a holistic approach to hair wellness, drawing upon ancestral wisdom to solve contemporary challenges. It is a story of continuity, where modern science often illuminates the ‘why’ behind practices long held sacred.

Granular clay, captured in stark monochrome, speaks to earth's embrace in holistic textured hair care rituals, echoing ancestral traditions in seeking natural ingredients. This close-up showcases a powerful formulation applied consciously for purification, nourishment, and revitalizing textured hair's inherent vitality.

How does Oil Application Support Holistic Hair Wellness through Ancestral Wisdom?

The concept of holistic wellness, deeply woven into many ancestral cultures, recognized that the health of the hair was connected to the health of the whole person. This comprehensive view often influenced traditional hair care regimens. The practice of oiling the scalp, a ritual common across African and South Asian traditions, was not only for the hair itself but also for invigorating the scalp, promoting blood flow, and creating a balanced environment for growth. This connection between scalp health and hair vitality is a timeless truth that modern understanding affirms.

For generations, particularly within Black communities, the act of applying oil or “greasing” the scalp was a foundational aspect of care, a cherished memory often tied to a grandmother’s or mother’s gentle hands. While some modern perspectives caution against excessive scalp oiling due to potential pore clogging, the underlying intention was always nourishment and protection. Many traditional applications were likely more sparse or used different formulations, or even applied to the hair itself rather than saturating the scalp with thick petroleum-based greases that came later. The original wisdom centered on providing a beneficial lipid barrier.

The age-old gesture of oiling textured hair, often an intimate moment of familial care, quietly speaks to a science of protection, ensuring the vitality of strands and honoring a shared past.

A powerful instance of this ancestral wisdom validating modern scientific insight comes from the widespread use of oils like coconut oil. Research has shown that coconut oil can reduce protein loss in hair. This scientific finding provides empirical backing to a practice that has existed for centuries in many cultures, including those with textured hair traditions, where coconut oil has been a staple for nourishing and protecting strands. This consistency across time and cultures highlights a profound, inherited understanding of how natural elements interact with hair structure.

The wisdom of traditional hair care, where oiling was an integral component, can be seen in its capacity to address common hair challenges, transforming them from problems into opportunities for mindful care.

  • Dryness ❉ Textured hair’s helical shape means sebum often struggles to travel down the strand. Oils seal in moisture, a practice evident in West African traditions where oils and butters kept hair hydrated in dry climates.
  • Breakage ❉ By lubricating the hair cuticle and sometimes penetrating the cortex, oils reduce friction and reinforce the hair’s structure, minimizing breakage from manipulation or environmental stressors. This aligns with protective styling history.
  • Environmental Damage ❉ Oils form a protective layer against sun exposure, wind, and pollution. The Himba tribe’s use of butterfat and ochre to guard against the sun is a historical testament to this.
This monochrome portrait immortalizes a woman's powerful gaze and distinctive coily afro, juxtaposed with a modern undercut, echoing heritage and identity. It celebrates a tapestry of expression, a nod to the beauty and resilience inherent in textured hair forms and styling choices within mixed-race narratives and holistic hair care.

How do Nighttime Rituals Safeguard Hair Using Oil?

Nighttime offers a unique opportunity for concentrated hair care, a practice deeply ingrained in the wisdom of our ancestors who understood the importance of protecting hair during rest. The simple ritual of covering hair with a bonnet or scarf, often after a light application of oil, serves as a profound act of preservation. This practice shields hair from friction against rough pillowcases, which can lead to breakage, split ends, and tangling for delicate textured strands.

The modern bonnet, whether silk or satin, descends from head coverings used by women of the diaspora for both practical and symbolic purposes. These coverings helped maintain intricate hairstyles for days or weeks, a necessity when daily washing was not feasible or desired. The underlying principle was protection.

Applying a modest amount of oil—perhaps a nourishing blend of jojoba and argan, which resemble natural sebum and provide antioxidants—before donning a bonnet helps to seal in moisture from the day’s conditioning treatments. This creates a closed, humid environment that allows the hair to remain supple and less prone to moisture loss overnight.

Consider the impact on the hair’s Lipid Content and overall health. While African hair naturally possesses a high lipid content, it is also prone to rapid moisture loss due to its unique structure. The external application of oils, particularly before protective wrapping, supplements these natural lipids and acts as an additional barrier against dehydration.

This strategic nightly care prevents the exacerbation of dryness that makes textured hair more susceptible to breakage, a cyclical challenge that generations have sought to address. The consistency of this ritual across countless households speaks to its proven effectiveness, a quiet testament to inherited knowledge.

Reflection

The strands that crown us carry stories, echoes of resilience, and silent testaments to ancestral wisdom. The simple act of applying oil, a gesture stretching back to the earliest known civilizations, stands as a quiet yet powerful thread connecting us to this profound heritage. It is a practice born of observation, need, and an intimate understanding of nature’s offerings, refined over millennia by hands that knew the subtle language of hair.

From the ceremonial oiling in ancient African societies to the purposeful applications in diasporic homes, this ritual has always been about more than mere surface conditioning. It has been about deep care, about preserving beauty against adversity, and about honoring the very fiber of identity.

As we come to understand the molecular dance of lipids and proteins, the protective shield formed against environmental elements, we realize that modern science often mirrors the intuitive knowledge of our forebears. The wisdom of applying oils to textured hair, securing its moisture, and safeguarding it from daily tolls, is not a trend but a continuation. It is a living archive, a constant reminder that the soul of a strand beats with the rhythm of ages, its vitality a legacy we continue to carry forward, one nourishing drop at a time. This enduring tradition, passed down through the generations, continues to shape how textured hair thrives, connecting us all to a deeper, richer understanding of its magnificent past and its luminous future.

References

  • Mohile, R. B. et al. Effect of mineral oil, sunflower oil, and coconut oil on prevention of hair damage. Journal of Cosmetic Science, 2003.
  • Campos, P. et al. Development and efficacy evaluation of hair care formulations containing vegetable oils and silicone. International Journal of Phytocosmetics and Natural Ingredients, 2011.
  • Nkwate, Jeanette. “Are We Really Not Supposed To Use Oils On Natural Hair?” Refinery29, 2022.
  • Balsara, Samira. “Understanding Hair Oiling ❉ History, Benefits & More.” Cécred, 2025.
  • Oforiwa, Alice. “The History and Culture of African Natural Hair ❉ From Ancient Times to Modern Trends.” AMAKA Studio, 2023.
  • Kari, A. “Scalp-Greasing ❉ A Black Hair Ritual.” GirlrillaVintage the Blog, 2017.
  • Perez, J. E. et al. The influence of hair lipids in ethnic hair properties. Journal of Cosmetic Science, 2023.
  • Almeida, C. J. et al. The Genomic Variation in Textured Hair ❉ Implications in Developing a Holistic Hair Care Routine. MDPI, 2023.
  • Crisps-Jackson, S. “The History of Textured Hair.” colleen, 2020.
  • Surjushe, A. et al. Scientific studies further confirm the pharmacological value of widely used plants such as Aloe vera and Curcuma domestica. (turmeric), which exhibit anti-inflammatory, antimicrobial, and wound-healing properties, supporting their continued use in traditional skincare systems. Indian Journal of Dermatology, Venereology, and Leprology, 2008.
  • Choudhury, N. et al. Plants used for hair and skin health care by local communities of Afar, Northeastern Ethiopia. Ethnobotany Research and Applications, 2025.
  • Mohammad, H. et al. Cosmetic Ethnobotany Used by Tribal Women in Epe Communities of Lagos State, Nigeria. Juniper Publishers, 2024.

Glossary

oil application

Meaning ❉ Oil Application, within the sphere of textured hair understanding, signifies the deliberate, measured placement of nourishing plant-derived lipids or specific blends onto the scalp and hair strands.

textured hair

Meaning ❉ Textured Hair, a living legacy, embodies ancestral wisdom and resilient identity, its coiled strands whispering stories of heritage and enduring beauty.

lipid content

Meaning ❉ The Lipid Content refers to the essential fatty substances within and on hair, crucial for its health, moisture, and protective barrier, particularly significant for textured hair.

coconut oil

Meaning ❉ Coconut Oil is a venerated botanical extract, deeply rooted in ancestral practices, recognized for its unique ability to nourish and protect textured hair, embodying a profound cultural heritage.

ancestral care

Meaning ❉ Ancestral Care, for those with textured hair, gently guides us to a discerning practice rooted in the enduring wisdom passed through generations, thoughtfully interpreted for contemporary understanding.

hair care

Meaning ❉ Hair Care is the holistic system of practices and cultural expressions for textured hair, deeply rooted in ancestral wisdom and diasporic resilience.

protective styling

Meaning ❉ Protective Styling is the ancestral practice of arranging hair to minimize manipulation and environmental exposure, preserving its health and affirming cultural identity.

natural oils

Meaning ❉ Natural oils refer to the sebum naturally produced by the scalp's sebaceous glands, a gentle, intrinsic gift for the well-being of textured hair.

moisture loss

Meaning ❉ Moisture Loss is the depletion of water from the hair strand, profoundly influenced by textured hair's unique structure and historical care traditions.

ancestral wisdom

Meaning ❉ Ancestral Wisdom is the enduring, inherited knowledge of textured hair's biological needs, its cultural significance, and its holistic care.

hair wellness

Meaning ❉ Hair Wellness is the holistic vitality of textured hair and scalp, deeply rooted in its rich cultural heritage and ancestral wisdom.

traditional hair care

Meaning ❉ Traditional Hair Care signifies ancestral practices and cultural wisdom for sustaining textured hair, deeply rooted in Black and mixed-race heritage.

scalp health

Meaning ❉ Scalp Health, for those tending to coils, curls, and waves, refers to the deliberate stewardship of the skin beneath the hair, establishing an optimal ground for vibrant hair development.

modern perspectives caution against excessive scalp

Modern science confirms clay's ancestral power to detoxify and nourish textured hair, balancing scalp ecosystems with its mineral richness.

ancestral wisdom validating modern scientific insight

Traditional African botanicals provide a scientific basis for hair integrity through their rich composition of beneficial compounds, validated by generations of textured hair heritage.

traditional hair

Meaning ❉ Traditional Hair signifies the inherent forms of textured hair and the ancestral care practices that honor its cultural and historical significance.

helical shape means sebum often struggles

Textured hair served as a means of resistance by embodying cultural heritage, facilitating covert communication, and symbolizing enduring identity.

these coverings helped maintain intricate hairstyles

Traditional oils protected textured hair from breakage and moisture loss, a practice deeply rooted in ancestral care and heritage.

perspectives caution against excessive scalp oiling

Cultural heritage shapes modern hair oiling by preserving ancestral wisdom, practices, and identity connections for textured hair care.

wisdom validating modern scientific insight comes

Climate adaptive oil use reveals textured hair heritage wisdom, offering insights into ancestral resilience and environmental harmony.

black hair

Meaning ❉ Black Hair describes the spectrum of hair textures primarily found within communities of African heritage, recognized by its distinct curl patterns—from expansive waves to tightly coiled formations—and an often elliptical follicle shape, which fundamentally shapes its unique growth trajectory.